Perimeter is the distance around a two-dimensional shape.

Example: the perimeter of this rectangle is 7+3+7+3 = 20

Example: the perimeter of this regular pentagon is:.

3 + 3 + 3 + 3 + 3 = 5×3 = 15

Perimeter Formulas

Try it yourself.

Helping with Math

What is a perimeter?

Perimeter is a closed path that covers or surrounds any two-dimensional shape . We can say that a perimeter is the total distance of any closed shape. Here are the examples of shapes that we can determine its perimeter. 

how to solve perimeter problem solving

How to find the perimeter?

Finding the perimeter of any two-dimensional shape depends on the number of sides our shape has. Say, for example, we have a triangle and a square. The number of sides a triangle has is 3; hence, we will get the total distance around its three sides. 

Now, how do we find the perimeter? Well, we need to start identifying the shape of our figure first, then use a formula in getting the perimeter. Each shape has a different formula in determining the perimeter – and that’s what we will tackle in the next sections.

The perimeter of a circle is called as the circumference . A circle is still considered a two-dimensional shape even though it does not have a length and width. However, they have radius and diameter . We can determine the circumference of any circle through its radius or diameter. 

Finding the Perimeter of a Circle through Radius

how to solve perimeter problem solving

The radius is the distance from the center of the circle to any point on the circumference. The image shows the radius of a circle.  

Now, to get the circumference of a circle using its radius, we will use the formula

where C = circumference,

    = 3.14 or $\frac{22}{7}$

    r = radius

What is the circumference of a circle if the radius is 18 cm? 

Solution 

Find the total distance around the circle with a radius that measures 30 meters. 

Finding the Perimeter of a Circle through its Diameter

how to solve perimeter problem solving

The diameter is the longest line segment in any circle. The measure of a diameter is twice the measure of a radius. Hence, the formula of finding the circumference of a circle through its diameter is given by:

= 3.14 or $\frac{22}{7}$

d = diameter

Example #1 

What is the circumference of a circle with a diameter of 13 mm? 

Determine the total distance around the circle when the diameter is 46 decimeters. 

how to solve perimeter problem solving

A triangle is a two-dimensional closed shape with three straight sides. Every triangle has three sides, three vertices, and three angles . If given a triangle, we simply add all the measures of its sides. 

The formula in finding the perimeter of a triangle is given by 

P = a + b + c

where a, b, and c are the measures of the sides of a triangle. 

If the measures of the sides of a triangle are 17 cm, 23 cm, and 25 cm, what is its perimeter? 

Can you determine the perimeter of a triangle if all three sides measure 19 meters?

Quadrilaterals 

A quadrilateral is any polygon with exactly four sides. There are different kinds of quadrilaterals such as square, rhombus , rectangle, trapezoid , and rhombus. 

how to solve perimeter problem solving

A square is a quadrilateral where each of its sides is equal. Hence, we can get the perimeter of a square by adding the measures of all four sides or by simply multiplying the measure of one side by 4.

Thus, the formula of finding the perimeter of the square is: 

where s is the measure of the side of a square. 

What is the perimeter of a square where each side measures 10 centimeters? 

Determine the total distance around a square where one side measures 27 meters.

how to solve perimeter problem solving

Like squares, a rhombus is a quadrilateral where four sides are equal, and the pair of opposite sides are parallel to each other. Hence, the formula in finding the perimeter of a rhombus is the same as finding the perimeter of a square. 

Thus, it is given by the formula

where s is the measure of the side of a rhombus. 

What is the perimeter of a rhombus if the measure of one side is 9 units?

Find the total distance of a rhombus with a side measure of 35 kilometers.

how to solve perimeter problem solving

A rectangle is a two-dimensional quadrilateral where opposite sides are parallel and equal. The sides of a rectangle are called as a width and length. Thus, the formula given in getting the perimeter of a rectangle is:

P = 2( l + w)

where l = length

What is the perimeter of a rectangle if the length measures 19 centimeters and the width measures 21 centimeters?

Determine the perimeter of a rectangle if the length measures 350 centimeters and the width measures 3 meters.

how to solve perimeter problem solving

Regular Polygon

Regular polygons are two-dimensional geometric figures with a fixed number of sides and where all sides are equal. 

Hence, the formula of finding the perimeter of any regular polygon is given by:

where n = number of sides of a regular polygon

s = measure of the side of a regular polygon

What is the perimeter of a 9-sided polygon with side measures of 23 meters?

Determine the perimeter of a five-sided regular polygon where each side measures 11 centimeters. 

What is the formula for finding the perimeter of some closed-shape?

The table below shows the formula for finding the perimeter of some closed-shape.

How to solve problems involving perimeter?

To solve problems that involve finding the perimeter of any closed shape , you may follow the following steps:

  • Identify the shape being described.
  • Make sure that the unit of measurement is always the same.
  • Use the formula for finding the perimeter of the given shape.
  • Always remember to write the proper unit of measurement. 

A rectangular field garden measures 45 yards by 60 yards. What is the total distance that surrounds the garden?

The diameter of a clock measures 10 inches. What is the circumference of the clock?

A seven-sided regular polygon with a side measure of 13 decimeters is needed for Gwyneth’s project. What is the total distance that surrounds the polygon? 

What is the importance of finding the perimeter?

The use of perimeter is used in our daily lives, especially architects and engineers. Most people who understand the concept of the perimeter can help them design their room , remodel their kitchen , or even build a table or chair . Farmers, gardeners, or even lot owners also use their knowledge in perimeter to fence their lots. More so, perimeters are important in estimating and calculating materials needed for completing a certain projects.

Recommended Worksheets

Perimeter of a Pentagon (Valentine’s Day Themed) Math Worksheets Perimeter of a Hexagon (Rio Carnival Themed) Math Worksheets Perimeter of Trapezoid (Lantern Festival Themed) Math Worksheets

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Perimeter – Definition, Regular and Irregular Shapes, Examples

What is a perimeter, how to find perimeter, solved examples on perimeter, practice problems on perimeter, frequently asked questions on perimeter.

In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.

Let’s try to calculate the perimeter of the following shape:

Perimeter of a shape = Sum of all its sides,

Perimeter of a shape = Sum of all its sides,

Perimeter of the given shape = 6 cm + 5 cm + 5 cm + 4 cm + 3 cm = 23 cm.

Determine the Perimeter Game

Perimeter of a Regular Shape

We know that the length of each side of a regular polygon is the same. Therefore, Perimeter of regular polygon = sum of all its sides = number of sides ✕ length of one side.

For example, look at the given regular pentagon.

Perimeter of a Regular Shape

The perimeter of the given regular pentagon can be calculated as follows:

Number of sides = 5 Length of one side = 4 cm

Therefore, Perimeter = number of sides ✕ length of one side

= 5 ✕ 4 = 20 cm

The given table summarizes the formulas to find the perimeter of some regular polygons:

Perimeter of some regular polygons

Perimeter of An Irregular Shape

Since the sides of an irregular polygon may not all be the same in length, we use the general formula to find the perimeter of an irregular shape. Therefore, Perimeter of irregular polygon = sum of all sides.

Real – World Applications

We often use the concept of perimeter in real life. For example, when putting up Christmas lights around the house or when we want to put a fence around the backyard, we find its perimeter to know the length of wire we will need.

Real - World Applications of perimeter

                      

Example 1: What is the perimeter of the given figure?

Solved Example of perimeter

Solution:  

We know that the perimeter of a triangle is given by

Perimeter = a + b + c,

Where a, b, c = length of three sides.

For the given triangle,

Perimeter = 5 cm + 4 cm + 3 cm = 12 cm

Example 2: Calculate the perimeter of the following figure.

Perimeter of irregular pentagon

The given shape is an irregular pentagon.

The perimeter of this pentagon will be given by the sum of all its sides.

Perimeter = 2 cm + 3 cm + 3 cm + 4 cm + 5 cm = 17 cm

Example 3: What will be the perimeter of a rectangle with length 12 cm and breadth 5 cm?

We know that the perimeter of a rectangle is given by 

Perimeter = 2 ✕ (l + b),

Where l = length of the given rectangle, b = breadth of the given rectangle.

For the given rectangle, l = 12 cm, b = 5 cm.

Therefore, perimeter of given rectangle = 2 ✕ (12 + 5) = 2 ✕ 17 = 34 cm

Attend this Quiz & Test your knowledge.

Find the perimeter of a square that has sides of 40 cm in length each.

Calculate the perimeter of a rectangle with length = 30 cm and breadth = 14 cm., find the perimeter of a circle with radius = 7 cm., calculate the perimeter of the following figure:.

Perimeter – Definition, Regular and Irregular Shapes, Examples

How many sides are required to determine the perimeter of a regular heptagon?

We only require the length of one side to determine the perimeter of any geometric figure with sides of equal length, such as a regular heptagon. The area of a heptagon = 7 ✕ a, where a is the side length.

What is the difference between the perimeter and area of a 2-D shape?

Perimeter measures the length of the boundary of the shape. It is given by the sum of all sides of the shape. It is one-dimensional and expressed in linear units. 

Area, on the other hand, measures the space occupied by the shape. It is two-dimensional and is expressed in square units.

How can we find the perimeter of a polygon?

The most general way to find the perimeter of any polygon is to find the sum of all its sides. However, another way of finding the perimeter of a regular polygon is to multiply the number of its sides by the side length.

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The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle . Area and perimeter are the two major properties of a 2D shape , which describes them.

The perimeter of each shape varies as per their dimensions. Only in the case of a circle, the perimeter is stated as the circumference of the circle . But the method to find the perimeter of all the polygons is the same, which is we need to add all its sides.

If we need to calculate the length of a circular or rectangular field, then with the help of the perimeter formula we can easily find it, given the dimensions. Let us learn the formula here to find the perimeter for all the two-dimensional shapes.

Also, read:

  • Area and Perimeter Formula
  • Perimeter Of Shapes
  • Perimeter Of Polygons

Perimeter Meaning

The perimeter of any two-dimensional closed shape is the total distance around it. Perimeter is the sum of all the sides of a polygon, such as:

  • Perimeter of square = Sum of all four sides
  • Perimeter of rectangle = Sum of all four sides
  • Perimeter of triangle = Sum of all three sides

Here is the list of formulas of the perimeter for all the 2d-shapes.

How to Find Perimeter

There are different ways to find the perimeter of a given shape apart from the formulas given above. We can use a ruler to measure the length of the sides of a small regular shape such as square, rectangle, parallelogram, etc. The perimeter will be obtained by adding the measurements of the sides/edges of the shape. 

We can use a string or thread for small irregular shapes. In this case, place either a string or thread precisely along the figure’s boundary once. The total length of the string used along the border of the shape is its perimeter.

Perimeter Units

Units are essential when representing the parameters of any geometric figure. For example, the length of a line segment measured is 10 cm or 10 m, here cm and m represent the units of measurement of the length. Similarly, the units for perimeter are the same as for the length of the sides or given parameter. If the length of the side of a square is given cm, then the units for perimeter will be in cm. There is another case, where the dimensions are given in two different units such as length of a rectangle in ft and breadth in inches, then units for the perimeter of a rectangle will be ft, for this we need to convert both the measurements into ft.

We will solve here some of the example questions to understand how to find the perimeter of different shapes.

Question.1: What is the perimeter of an equilateral triangle whose side length is 7 cm?

Solution: Given, the length of the side of an equilateral triangle is 7 cm

As we know, the equilateral triangle has all its sides equal in length.

Perimeter of triangle = a+b+c

Perimeter = 3a

P = 3 x 7 = 21 cm

Question 2: If the length of parallel sides of a parallelogram is 8 cm and 11 cm, respectively, then find its perimeter.

The length of parallel sides of a parallelogram is 8 cm and 11 cm, respectively.

By the formula of perimeter, we know;

Perimeter of Parallelogram = 2(a+b)

P = 2 (8 + 11)

Therefore, the perimeter of a given parallelogram is 38 cm.

Question 3: If the radius of a circle is 21 cm, then find its perimeter.

Solution: Given,

Radius of circle = 21 cm

Perimeter of circle = Circumference of circle = 2πr

Circumference = 2 × 22/7 × 21

= 2 × 22 × 3

Therefore, the perimeter of the circle here is equal to 21 cm.

Question 4: A regular pentagon of side 3 cm is given. Find its perimeter.

Solution: Given, the length of the side of a regular pentagon = 3 cm

As we know, a regular pentagon will have all its 5 sides equal.

The perimeter of the regular pentagon = 5a, where a is the side length

Perimeter = 5 × 3

Therefore, the answer is 15 cm here.

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How to Find Perimeter

Last Updated: March 5, 2024 Fact Checked

This article was co-authored by Jake Adams and by wikiHow staff writer, Hannah Madden . Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University. There are 16 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 148,766 times.

The perimeter is the length of an outline of a shape. The general way to find the perimeter of any shape is to add up the length of all its sides. For certain shapes, such as rectangles and circles, there are specific formulas you can use to simplify the process. In other instances, you might be missing one or more of the side lengths, but are given other information. In cases like this, you must complete extra steps to find the missing side length before you can calculate the perimeter.

Calculating the Perimeter of a Shape

The find the perimeter of any shape, add up the length of all its sides. For specific shapes, such as rectangles and circles, just multiply the length of one side by the number of sides to get the total perimeter.

Perimeter Review

Step 1 Perimeter is defined as the length surrounding a given area.

  • You might not be given the length of all 4 sides, which is another reason why you’d need to use an equation to find the perimeter instead of just addition.

Step 2 Circumference is the perimeter of a circle.

  • You can’t find the perimeter of a circle just by measuring it; you have to use the circumference equation.

Step 3 Express the perimeter in distance units.

  • You’ll have to make sure all your units are the same before you do your equation, too. This might mean changing feet to inches, miles to feet, or anything in between.

Step 4 Use an online calculator to check your answer.

  • Make sure you’re using a calculator for your specific shape.

Finding the Perimeter of Rectangles (Including Squares)

Step 1 Set up the formula for the perimeter of a rectangle.

  • If you don’t know the height and width of your shape, you can plug in the information you do know, like the area, the length of one side, or the length of the diagonal.

Step 2 Plug the width and height into the formula.

Finding the Perimeter of a Circle

Step 1 Set up the formula for finding the circumference of a circle.

  • When finding the perimeter of a circle, you don’t use the term perimeter, you use circumference. This is because circles don’t have any straight lines.
  • Pi: A numerical constant, used in this formula to signify the constant numerical shape of a circle.
  • Diameter: The length of the line through the center of the circle that touches both edges.
  • Radius: The length of any line segment from the center of a circle out to the edge of the circle.

Step 2 Plug the length of the radius into the formula.

Finding the Perimeter of Triangles

Step 1 Set up the formula for finding the perimeter of a triangle.

  • For example, if an isosceles triangle has a height of 10 cm and a base of 6 cm, you can think of the height creating two right triangles. Since the height bisects the base, one side length of the right triangle will be 3 cm. The other side length will be equal to the height: 10 cm. The missing side length is the hypotenuse.

10^{{2}}+3^{{2}}=c^{{2}}

Finding the Perimeter of a Regular Polygon

Step 1 Find the length of one side.

Finding the Perimeter of an Ellipse

Step 1 Measure the “sides” of your ellipse.

  • Normally, variable a goes from left to right on the major axis, and variable b goes up and down on the minor axis.

Step 2 Plug the information into an equation.

  • This will give you an answer within 5% of the true perimeter of the ellipse.

{\displaystyle p=2\pi {\sqrt {(3^{2}+2^{2})/2}}.}

Finding the Perimeter of a Sector

Step 1 Find the length of the arc.

Finding the Perimeter of a Pentagon

Step 1 Find the number of sides and the length of one side.

Finding the Perimeter of a Quadrilateral

Step 1 Find the length of all 4 sides.

  • If you don’t know the length of all 4 sides, you can use the information you do have to solve for variable x.

Step 2 Plug the side lengths into your equation.

Community Q&A

Donagan

  • To find the perimeter of a trapezoid when you are missing side lengths, in general you want to divide the trapezoid into two right triangles and one rectangle. From there you can use the properties of right triangles and rectangles to find the missing side lengths. Thanks Helpful 0 Not Helpful 0
  • To find the perimeter of a rhombus when you are missing side lengths, in general you want to use the diagonal(s) of the rhombus to divide the shape into several right triangles. Then you can use the Pythagorean theorem or trigonometry to find the missing side lengths. Thanks Helpful 0 Not Helpful 0

how to solve perimeter problem solving

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Find the Perimeter of a Triangle

Expert Interview

how to solve perimeter problem solving

Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with Jake Adams .

  • ↑ https://sciencing.com/perimeter-circle-4487756.html
  • ↑ https://www.cuemath.com/geometry/circumference-of-a-circle/
  • ↑ https://www.omnicalculator.com/math/perimeter#how-to-find-perimeter-perimeter-formulas
  • ↑ https://www.mathsisfun.com/geometry/perimeter.html
  • ↑ https://www.mathsisfun.com/geometry/square.html
  • ↑ https://www.youtube.com/watch?v=EIWGr_NcnJA
  • ↑ http://www.mathplanet.com/education/pre-algebra/more-about-equation-and-inequalities/calculating-the-circumference-of-a-circle
  • ↑ http://mathworld.wolfram.com/EquilateralTriangle.html
  • ↑ http://www.varsitytutors.com/basic_geometry-help/how-to-find-the-perimeter-of-a-right-triangle
  • ↑ http://www.mathopenref.com/isosceles.html
  • ↑ http://www.mathopenref.com/polygonsides.html
  • ↑ http://www.mathopenref.com/polygonperimeter.html
  • ↑ https://www.mathsisfun.com/geometry/ellipse-perimeter.html
  • ↑ https://byjus.com/maths/sector-of-a-circle/
  • ↑ https://tutors.com/math-tutors/geometry-help/how-to-find-the-perimeter-of-a-pentagon
  • ↑ https://www.math-only-math.com/perimeter-of-quadrilateral.html

About This Article

Jake Adams

The right way to find perimeter depends on the shape you're working with. For rectangles, use the formula p = 2 (w + h), where w is the width of the rectangle and h is the height. To find the perimeter of a square, use the formula p = 4x, where x is the length of 1 side of the square. If you need to find the perimeter of a triangle, use the formula p = a + b + c, where a, b, and c are the lengths of the 3 sides of the triangle. Finally, to find the perimeter of a circle, use the formula c = π (d), where c is the perimeter and d is the diameter. If you want to learn how to find the perimeter of any regular polygon, keep reading the article! Did this summary help you? Yes No

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Word Problems: Area and Perimeter of a Rectangle

In geometry, calculating the area and perimeter of rectangles is typically one of the first lessons we learn. While some of us may find this concept easy, it's worth noting that these skills have real-world applications. Math is not solely for theoretical problem-solving on paper; it can also help us gain valuable insights about the world around us. We will explore how to solve word problems related to finding the area and perimeter of a rectangle.

Review: What is a rectangle?

As you might recall, a rectangle is a parallelogram with four right angles. While a rectangle falls into the general category of a parallelogram, not all parallelograms are rectangles. Interestingly enough, squares are also considered rectangles -- but not all rectangles are squares. This is what a typical rectangle looks like:

Review: Finding the perimeter and area of a rectangle

Let's quickly review how to find the perimeter of a rectangle.

As we may recall, the formula for finding the perimeter is quite simple: P = 2 l + 2 w where P is the perimeter, l is the length, and w is the width.

We may also recall that the formula for area is A = l ⁢ w

Things really start to get tricky when we are only given certain values, and we need to find the missing values. These questions can be more difficult than they seem at first.

Solving word problems

Now we're ready to start solving some word problems with our knowledge of rectangle perimeter and area:

Let's assume that we have a swimming pool with a perimeter of 56 meters. We also know that the length of the pool is 16 meters. Can we use these values to determine the width of our pool?

Let's start by visualizing the problem:

Next, let's remind ourselves of the formula for perimeter: P = 2l+2w

Now let's plug in our known values: f o r m u l a = 2 ( 1 6 ) + 2 w

Now we can simplify: formula56 = 32 + 2 w

Next, we can simplify even further by subtracting 32 from both sides: f = a ⁢ x ⁢ b c ⁢ x ⁢ d

Now all we need to do is ask ourselves what value equals 24 when multiplied by two. In other words, we need to divide both sides of the equation by 2. We are left with: w = 12

The width of this pool must be 12 meters.

Let's try another question:

Let's say we have a rectangular fence. We know that this fence encloses an area of 500 square feet. We also know that the width of this fenced enclosure is 20 feet. Using these values, can we determine the length of the fence?

First, let's visualize the problem:

Next, let's remind ourselves of the formula for the area of a rectangle: A = l ⁢ w

Now all that we need to do is divide each side of the equation by 20 to isolate and determine the length f = 25 .

In other words, the length of our rectangular fenced enclosure is 25 feet.

Topics related to the Word Problems: Area and Perimeter of a Rectangle

Word Problems

Flashcards covering the Word Problems: Area and Perimeter of a Rectangle

4th Grade Math Flashcards

Common Core: 4th Grade Math Flashcards

Practice tests covering the Word Problems: Area and Perimeter of a Rectangle

Common Core: 4th Grade Math Diagnostic Tests

4th Grade Math Practice Tests

Pair your student with a tutor who can explain word problems involving rectangular areas and perimeters

It can be difficult for students to fully grasp concepts like rectangular areas and perimeters. This is especially true when dealing with word problems, as some students process visual information better than verbal information, and vice versa. One of the key benefits of tutoring is the fact that these educators can present information in a way that is conducive to your student's learning style. For example, visual learners can draw out the problem, while verbal learners can talk the problem through with their tutors. Tutors can also personalize your student's learning experience in a number of different ways based on their ability level and even their hobbies. Each tutor is carefully vetted before working with students, ensuring a high level of academic knowledge and teaching skill. Reach out to Varsity Tutors today, and we'll pair your student with an appropriate tutor.

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Perimeter Calculator

What is perimeter, how to find perimeter – perimeter formulas, perimeter of a square formula, formula for the perimeter of a rectangle, perimeter of a triangle formula, perimeter of a circle formula (circumference formula), perimeter of a circle sector formula, perimeter of an ellipse formula (ellipse circumference formula), perimeter of a trapezoid formula, perimeter of a parallelogram formula, perimeter of a rhombus formula, perimeter of a kite formula, perimeter of an annulus formula, perimeter of a polygon formula (regular pentagon, hexagon, octagon, etc.).

With this perimeter calculator, you don't need to worry about perimeter calculations anymore. Below you'll find the perimeter formulas for twelve different shapes, as well as a quick reminder about what a perimeter is and a perimeter definition. Read on, give it a try, or check this calculator's twin brother – our comprehensive area calculator .

Perimeter is the boundary of a closed geometric figure . It may also be defined as the outer edge of an area, simply the longest continuous line that surrounds a shape. The name itself comes from Greek perimetros : peri meaning "around" + metron , understood as "measure". As it's the length of the shape's outline, it's expressed in distance units – e.g., meters, feet, inches, or miles.

the same area for different shapes

Usually, the most simple and straightforward approach is to find the sum of all of the sides of a shape . However, there are cases where there are no sides (such as an ellipse, circle, etc.), or one or more sides are unknown. In this paragraph, we'll list all of the equations used in this perimeter calculator.

Scroll down to the next sections if you're curious about a specific shape, and wish to see an explanation, derivation, and image for each of the twelve shapes present in this calculator. We also have tools dedicated to each shape – just type the name of the shape in the search bar at the top of this webpage.

Here are the perimeter formulas for the twelve geometric shapes in this calculator:

Square perimeter formula: P = 4 a P = 4a P = 4 a .

Rectangle perimeter formula: P = 2 ( a + b ) P = 2(a + b) P = 2 ( a + b ) .

Triangle perimeter formulas:

  • P = a + b + c P = a + b + c P = a + b + c ; or
  • P = a + b + a 2 + b 2 − 2 a b × cos ⁡ ( γ ) P = a + b + \sqrt{a^2 + b^2 - 2ab \times \cos(\gamma)} P = a + b + a 2 + b 2 − 2 ab × cos ( γ ) ​ ; or
  • P = a + a sin ⁡ ( β + γ ) × ( sin ⁡ ( β ) + sin ⁡ ( γ ) ) P = a + \frac{a}{\sin(\beta + \gamma)} \times (\sin(\beta) + \sin(\gamma)) P = a + s i n ( β + γ ) a ​ × ( sin ( β ) + sin ( γ )) .

Circle perimeter formula: P = 2 π r P = 2\pi r P = 2 π r .

Circle sector perimeter formula: P = r ( α + 2 ) P = r(\alpha + 2) P = r ( α + 2 ) ( α \alpha α is in radians);

Ellipse perimeter formula: P = π [ 3 ( a + b ) − ( 3 a + b ) × ( a + 3 b ) ] P = \pi\bigl[3(a + b) - \sqrt{(3a + b) \times (a + 3b)}\bigl] P = π [ 3 ( a + b ) − ( 3 a + b ) × ( a + 3 b ) ​ ] ;

Quadrilateral / Trapezoid perimeter formula: P = a + b + c + d P = a + b + c + d P = a + b + c + d .

Parallelogram perimeter formulas:

  • P = 2 ( a + b ) P = 2(a + b) P = 2 ( a + b ) ;
  • P = 2 a + 2 e 2 + 2 f 2 − 4 a 2 P = 2a + \sqrt{2e^2 + 2f^2 - 4a^2} P = 2 a + 2 e 2 + 2 f 2 − 4 a 2 ​ ; or
  • P = 2 ( b + h / sin ⁡ ( α ) ) P = 2(b + h/\sin(\alpha)) P = 2 ( b + h / sin ( α )) .

Rhombus perimeter formulas:

  • P = 4 a P = 4a P = 4 a ; or
  • P = 2 e 2 + f 2 P = 2\sqrt{e^2 + f^2} P = 2 e 2 + f 2 ​ .

Kite perimeter formula: P = 2 ( a + b ) P = 2(a + b) P = 2 ( a + b ) .

Annulus perimeter formula: P = 2 π ( R + r ) P = 2\pi(R + r) P = 2 π ( R + r ) .

Regular polygon perimeter formula: P = n × a P = n \times a P = n × a .

A square has four sides of equal length. To calculate its perimeter, all you need to do is to multiply the side length by 4 4 4 :

Believe it or not, but we have a perimeter of a square calculator , too!

The formula for the perimeter of a rectangle is almost as easy as the equation for the perimeter of a square. The only difference is that we have two pairs of equal-length sides:

The easiest formula to calculate the perimeter of a triangle is – as usual – by summing all sides:

However, you aren't always given three sides. What can you do then? Well, instead of fretting, you can use the law of cosines calculator to find the missing side:

This can be incorporated into the perimeter formula:

The other option is to use the law of sines if you have one side and the two angles that are adjacent to that side:

so the triangle perimeter may be expressed as:

A perimeter of a circle has a special name – it's also known as the circumference . The most well-known perimeter of a circle formula uses only one variable – circle radius:

Have you ever wondered how many times your bike wheel will rotate on a ten-mile trip? Well, that's one of the cases where you'll need to use the circumference formula. Input the radius of your wheel (half of the wheel's diameter), and divide 10 miles by the obtained circumference (but don't forget about the conversion of the units of length!). If you want to be even more accurate, you can include the size of the bike tire.

Calculating the perimeter of a circle sector may sound tricky – is it only the arc length, or is it the arc length plus two radii? Just keep in mind the perimeter definition! The sector perimeter is the sum of the lengths of all its boundaries, so it's the latter:

where α \alpha α is in radians.

Although the formula for the area of an ellipsis really simple and easy to remember, the perimeter of an ellipse formula is the most troublesome of all the equations listed here. We've chosen to implement one of the Ramanujan approximations in this perimeter calculator:

Where a a a is the shortest possible radius and b b b in the longest possible radius of an ellipse. The other, more accurate Ramanujan approximation is:

There is also a simpler form, using an additional variable h h h :

Or you could just use our calculator!

If you want to calculate the perimeter of an irregular trapezoid, there's no special formula – just add all four sides:

Maybe you've noticed, but it's the formula for any quadrilateral perimeter.

There's also an option that presents itself with certain special trapezoids – like an isosceles trapezoid, where you need a a a , b b b , and c c c sides. Another example is a right trapezoid, where the length of the bases and one leg are enough to find the shape's perimeter (to find the last leg, we calculate Pythagoras' Theorem).

In this perimeter calculator, you'll find three formulas to calculate the perimeter of a parallelogram:

  • The most straightforward one, adding all sides together:
  • The perimeter of a parallelogram formula that requires one side and diagonals
  • The perimeter is given in terms of base, height, and any parallelogram angle .

The perimeter of a rhombus formula is not rocket science, so let's make it concise – it's the same as the perimeter of a square formula!

Another solution to finding the rhombus perimeter requires the diagonal lengths:

Try deriving the formula yourself. You know that the two diagonals of a rhombus are perpendicular to and bisect each other so that you can divide the shape into four congruent right triangles. Each triangle has legs that are e/2 and f/2 long – all you need to do is find the triangle's hypotenuse, which is, at the same time, the rhombus side. Then multiply the result by four to find the final perimeter of a rhombus formula.

The formula for the perimeter of a kite is pretty straightforward – just sum up all of the sides:

As the perimeter is defined as the boundary, an annulus requires us to add the circumference of both concentric circles:

In our perimeter calculator, we've also implemented a simple formula for a regular polygon perimeter:

where n n n is the number of polygon sides. So, for example, you can calculate the perimeter of a pentagon, hexagon, or octagon.

Additionally, for polygons up to 12 sides, the polygon name will appear in the tool. Awesome!

If you want to determine the perimeter of any polygon, sum the lengths of all its sides:

where a 1 a_1 a 1 ​ , a 2 a_2 a 2 ​ , ..., a n a_n a n ​ are sides lengths, and ∑ \sum ∑ is the sum symbol (from i = 1 i = 1 i = 1 to n n n ).

Or use the vertices coordinates:

With x n + 1 = x 1 x_{n+1}=x_1 x n + 1 ​ = x 1 ​ and y n + 1 = y 1 y_{n+1}=y_1 y n + 1 ​ = y 1 ​ .

How do I calculate the perimeter of irregular shapes?

To find the perimeter of an irregular figure:

  • Measure the lengths of all (outer) sides.
  • If the sides include circular fragments , measure the radius and the central angle, i.e., the angle between the radii that join the two endpoints of the arc to the center.
  • Apply the circle circumference formula for this radius and take the part proportional to the angle.
  • Add together the length of all sides.

Can I determine area given perimeter?

In general, no , it's not possible to calculate area from the perimeter. This is particularly true for rectangles, parallelograms, kites, and trapezoids. However , for some specific shapes, like squares, hexagons, regular polygons in general, and circles, you can determine their side (radius in the case of circles) from the perimeter and then proceed to compute the area.

What is the perimeter of a 20m by 15m rectangular building?

The perimeter is 70 m . To arrive at this result, you need to add together the length of all four sides of the building. Two sides of length 20 m added together give 40 m, while the other two sides of length 15 m added together give 30 m. Together, we get 40 m + 30 m = 70 m, as claimed.

Area of crescent

Christmas tree, rise over run, secretary problem (valentine's day).

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Course: Algebra 2   >   Unit 12

Manipulating formulas: perimeter.

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COMMENTS

  1. How to Find Perimeter in 3 Easy Steps

    Step #1: Identify the Shape. Step #2: Identify all of the side lengths and add them together. Step #3: Determine the perimeter and use appropriate units of measurement. Let's go ahead and apply these three steps to this first example of how to find perimeter of a square. Step #1: Identify the Shape.

  2. Perimeter & area (video)

    Perimeter is the distance around the outside of a shape. For example, if you walk around the edge of a playground, you're measuring its perimeter. Area is the amount of space inside a shape. For example, if you want to put new tiles on your kitchen floor, you need to know the area of the room to know how many tiles to buy.

  3. Perimeter of a Rectangle Word Problems

    Find the perimeter of the rectangle both in feet and inches. This problem is asking us to express the perimeter of the rectangle using two different units of measurement, i.e. in feet and in inches. To get both measurement units, we'll solve the problem in two parts. PART 1: Express the perimeter of the rectangle in feet.

  4. Perimeter Word Problems

    Concept Development. Problem 1: Solve perimeter word problems with rectangles. Mrs. Kozlow put a border around a 5-foot by 6-foot rectangular bulletin board. How many feet of border did Mrs. Kozlow use? Problem 2: Solve perimeter word problems with regular polygons.

  5. Perimeter: introduction (video)

    Perimeter: introduction. Perimeter is a math concept that measures the total length around the outside of a shape. To find the perimeter, you add together the lengths of all the sides. This works for any shape, including triangles, rectangles, pentagons, and even irregular polygons. Created by Sal Khan.

  6. Perimeter

    Perimeter is the distance around a two-dimensional shape. Example: the perimeter of this rectangle is 7+3+7+3 = 20. Example: the perimeter of this regular pentagon is: 3 + 3 + 3 + 3 + 3 = 5×3 = 15. The perimeter of a circle is called the circumference: Circumference = 2 π × radius.

  7. Area and perimeter

    Test your understanding of Area and perimeter with these NaN questions. Start test. Area and perimeter help us measure the size of 2D shapes. We'll start with the area and perimeter of rectangles. From there, we'll tackle trickier shapes, such as triangles and circles.

  8. Perimeter

    Explanation. P = a + b + c. Write the formula for finding the perimeter of any triangle. P = 19 m + 19 m + 19 m. Since the sides of the triangle are equal, we will simply add 19 three times. Alternatively, we can get the perimeter of an equilateral triangle by multiplying the measure of the side by 3.

  9. Finding the Perimeter

    Learn how to find perimeter with Mr. J. Whether you're just starting out, need a quick refresher, or here to master your math skills, this is the place for s...

  10. How To Find Perimeter? Definition, Formulas, Examples, Facts

    Perimeter = 5 cm + 4 cm + 3 cm = 12 cm. Example 2: Calculate the perimeter of the following figure. Solution: The given shape is an irregular pentagon. The perimeter of this pentagon will be given by the sum of all its sides. Perimeter = 2 cm + 3 cm + 3 cm + 4 cm + 5 cm = 17 cm. Example 3: What will be the perimeter of a rectangle with length ...

  11. Perimeter Word Problems: Examples

    Math Worksheets. Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to solve word problems that involve perimeter. Perimeter Word Problem. Example: The length of a rectangle is 8 cm more than 3 times its width. The perimeter of the rectangle is 64 cm. Find the area of the rectangle.

  12. Perimeter (Meaning, Formula, Units, Calculation & Solved Examples)

    By the formula of perimeter, we know; Perimeter of Parallelogram = 2 (a+b) P = 2 (8 + 11) P = 2 x 19. P = 38 cm. Therefore, the perimeter of a given parallelogram is 38 cm. Question 3: If the radius of a circle is 21 cm, then find its perimeter. Solution: Given, Radius of circle = 21 cm.

  13. Perimeter: Problems with Solutions

    Problem 6. A rectangle has a length of 28 cm and a width smaller by 6 cm. Its perimeter is cm. Problem 7. A rectangle has a width of 19 cm and a length three times greater than its width. Its perimeter is cm. Problem 8. The width and length of a rectangle are two consecutive numbers. If the perimeter is 30 cm, then its width is cm.

  14. 9 Ways to Find Perimeter

    A square has 4 equal sides, so to find its perimeter, you only need to multiply the length of one side by 4. [6] For example, if a square has one side that is 3 cm long, to find the perimeter, you would calculate . So, the perimeter is 12 cm. 5. Find the perimeter given other information.

  15. Area and perimeter word problems (practice)

    Area & perimeter word problem: dog pen. Video 4 minutes 46 seconds 4:46. Area & perimeter word problem: table . Report a problem. ... Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class ...

  16. Perimeter Word Problems Worksheet

    When calculating the perimeter of a rectangle, we can add up the lengths of all the sides or we can use the formula. P = 2 (l + w) where P is the perimeter, l is the length, and w is the width. This formula works because a rectangle has two pairs of parallel sides, and each pair has the same length. Therefore, to find the perimeter, you can add ...

  17. Word Problems: Area and Perimeter of a Rectangle

    This is what a typical rectangle looks like: Let's quickly review how to find the perimeter of a rectangle. As we may recall, the formula for finding the perimeter is quite simple: P = 2 l + 2 w where P is the perimeter, l is the length, and w is the width. We may also recall that the formula for area is A = l. ⁢.

  18. How to Solve Word Problems Involving Perimeter

    Solve Word Problems Involving Perimeter. Step 1: Read the given word problem and identify the dimensions that are given. Step 2: Find the dimensions that are not given. Use these tips to find the ...

  19. Perimeter Calculator

    Perimeter is the boundary of a closed geometric figure.It may also be defined as the outer edge of an area, simply the longest continuous line that surrounds a shape. The name itself comes from Greek perimetros: peri meaning "around" + metron, understood as "measure".As it's the length of the shape's outline, it's expressed in distance units - e.g., meters, feet, inches, or miles.

  20. Manipulating formulas: perimeter (video)

    Video transcript. We are told that the formula for finding the perimeter of a rectangle is P is equal to 2l plus 2w, where P is the perimeter, l is the length, and w is the width. And just to visualize what they're saying, and you might already be familiar with this, let me draw a rectangle. That looks like a rectangle.

  21. Algebra: Perimeter Word Problems

    Perimeter of Hexagon Word Problem with algebra. Example: The length of each side of a hexagon is 6 inches less than the length of a side of a square. The perimeter of the hexagon is equal to the perimeter of the square. Find the length of a side of the hexagon and the length of a side of the square. Try the free Mathway calculator and problem ...

  22. Equations: Perimeter/Angles Textbook Exercise

    Click here for Questions . forming, creating, perimeter, angles, solving. Textbook Exercise. Previous: Equations: Letters on Both Sides Textbook Exercise

  23. Step-by-Step Math Problem Solver

    QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...