how to solve perimeter problem solving

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 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

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

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. 

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. 

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.

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.

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.

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.

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

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.

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 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.

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

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.

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:.

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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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.

• Math Article

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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Perimeter of a square

Here you will learn how to find the perimeter of a square, including what the perimeter is, how to calculate it and how to solve perimeter word problems.

Students will first learn how to find perimeter as part of measurement and data in 3 rd grade.

What is perimeter of a square?

The perimeter of a square is the total distance around the outside of the square.

For example,

Perimeter is measured in units. Each side of the square is one unit.

The perimeter of the square is found by counting the units on each side of the square. You can do this by starting at a vertex and counting each unit until you arrive back at the vertex.

There are 16 units around the outside of the square, so the perimeter is 16 units.

Notice the perimeter can also be calculated by adding the length of each side.

4 + 4 + 4 + 4 = 16 , so the perimeter is 16 units.

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter.

4 \text { units } \times 4=16 \text { units }

The general perimeter of a square formula is \, 4 \, \times \text { side length } or \, 4s .

Common Core State Standards

How does this relate to 3 rd grade math?

• Grade 3 – Measurement and data (3.MD.D.8) Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

How to find the perimeter of a square

In order to calculate the perimeter of a square:

• Add all the side lengths.
• Write the final answer with the correct units.

[FREE] Perimeter Check for Understanding Quiz (Grade 3 to 4)

Use this quiz to check your grade 3 to 4 students’ understanding of perimeter. 10+ questions with answers covering a range of 3rd and 4th grade perimeter topics to identify areas of strength and support!

Perimeter of a square examples

Example 1: gridded square.

What is the perimeter of the square?

This side of the square is 3 units. This means every side of the square is 3 units.

To find the perimeter (the total distance around the square), add all the side lengths:

3 + 3 + 3 + 3 = 12

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 3 \times 4=12.

2 Write the final answer with the correct units.

There are no specific units given, so they are just labeled ‘units.’

The perimeter of the square is 12 units.

Example 2: gridded square

This side of the square is 5 units. This means every side of the square is 5 units.

5 + 5 + 5 + 5 = 20

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 5 \times 4=20 .

The perimeter of the square is 20 units.

Example 3: non-gridded square

One side of the square is 7 feet. This means every side of the square is 7 feet.

7 + 7 + 7 + 7 = 28

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 7 \times 4=28 .

The side lengths are measured in feet, so the total perimeter is in feet.

The perimeter of the square is 28 feet.

Example 4: non-gridded square

One side of the square is 13 {~cm} . This means every side of the square is 13 {~cm} .

13 + 13 + 13 + 13 = 52

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 13 \times 4=52 .

The side lengths are measured in centimeters, so the total perimeter is in centimeters.

The perimeter of the square is 52 centimeters.

Example 5: perimeter word problem

Nya has a square shaped garden. She wants to put a fence around the garden. If one side of the garden is 16 feet, how many feet of fencing does she need to surround the garden?

One side of the square is 16 {~ft} . This means every side of the square is 16 {~ft} .

16 + 16 + 16 + 16 = 64

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 16 \times 4= 64.

The perimeter of the square garden is 64 feet, so Nya needs 64 feet of fencing.

Example 6: given perimeter – find missing side length

The perimeter of the square is 44 {~m} . What are the side lengths?

Remember, all the sides of the square are congruent (equal).

So, the perimeter is the same number added 4 times:

? \; + \; ? \; + \; ? \; + \; ? = 44 \, m

Another way to think about it is ? \times 4=44.

Since 11+11+11+11= 44 and 11 \times 4= 44 , the side length of the square is 11 .

The square is measured in meters (m) .

The missing side length is 11 {~m} .

Teaching tips for the perimeter of a square

• Use worksheets that have a mixture of gridded or non-gridded squares and word problems (with and without a visual), so students can practice all perimeter solving strategies. This also challenges them to decide which strategies are most useful in different circumstances.
• Encourage students to look for patterns and extend patterns when finding the area of a square. Students are never too young to notice relationships and generalize patterns. This will also help them make sense of the formula 4 s .

Easy mistakes to make

• Thinking the order of adding the sides matters It doesn’t matter the order in which the sides of the shape are added, because of the commutative property of addition. As long as all sides are added only once, they can be added in any order.
• Confusing the formulas or solving strategies for perimeter with area It is easy to confuse these two concepts, especially when first learning them. Remember that perimeter is the measurement of the length around a square (one-dimensional) and area is the measurement of the space within a square (two-dimensional).
• Adding uncommon units Side lengths must be in the same units before they can be added. This means the unit squares must be the same size or the lengths given must all be in the same unit (for example, all measurements given are in {~cm} ). If the sides are shown in different units, convert them to be a common unit before adding.

Related perimeter lessons

• How to find perimeter
• Perimeter of a rectangle
• Perimeter of a triangle

Practice perimeter of a square questions

1) What is the perimeter of the square?

The length of a side is 6 units. Since a square has equal sides, all side lengths are 6 .

6 + 6 + 6 + 6 = 24

You can also multiply one side length by 4 to calculate the perimeter:

4 \times 6=24.

The perimeter of the square is 24 units.

2) Which square has a perimeter of 8 units?

Since the perimeter is 8 units, the sum of the lengths of all the sides is 8 .

That means the length of each side of the square must be 2 units, since

2 + 2 + 2 + 2 = 8.

You can also think about what number times 4 is equal to 8 : 4 \, \times \, ?= 8.

Since 4 \times 2= 8, the square has side lengths of 2 units.

3) What is the perimeter of the square?

The sides are all equal lengths, so to calculate the perimeter (the total distance around the square), add them:

8 + 8 + 8 + 8 = 32

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 4 \times 8= 32 .

The side lengths are measured in millimeters, so the total perimeter is in millimeters.

The perimeter of the square is 32 {~mm} .

4) What is the perimeter of the square?

23 + 23 + 23 + 23 = 92

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 4 \times 23= 92.

The side lengths are measured in meters, so the total perimeter is in meters.

The perimeter of the square is 92 {~m} .

5) A hotel has a square pool. One side of the pool is 24 feet. What is the perimeter of the pool?

The length of the side is the same, so to calculate the perimeter (the total distance around the square), add them:

24 + 24 + 24 + 24 = 96

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 4 \times 24= 96 .

The perimeter of the square is 96 {~ft} .

6) The perimeter of the square is 60 {~cm} . What is the length of its sides?

? \; + \; ? \; + \; ? \; + \; ? = 60 {~cm}

Another way to think about it is ? \times 4= 60.

Since 15 + 15 + 15 + 15= 60 and 15 \times 4= 60 , the side length of the square is 15.

The square is measured in centimeters (cm) .

The missing side length is 15 {~cm} .

Perimeter of a square FAQs

Perimeter is the total length around a square and is measured in units. Area of the square is the space within a rectangle and is measured with square units. They represent different parts of a square, but both require knowing the dimensions of a side to solve.

Just like with squares, you add the 4 side lengths up to find the total distance around the quadrilateral. However, unless the shape is a square or a rhombus, not all sides will be equal. The perimeter of rectangles, parallelograms, and trapezoids can have different side lengths.

The next lessons are

• Angles in polygons
• Congruence and similarity
• Prism shape

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