## Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

## Geometry Word Problems Involving Perimeter

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

Step 3: Plug in the values from the question and from the sketch.

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

## Geometry Math Problem involving the perimeter of a rectangle

## Geometry Math Problem involving the perimeter of a triangle

## Geometry Practice Questions

2. What is the area of a circle with a diameter of 16?

3. The figure below contains only horizontal and vertical lines. Calculate its perimeter.

4. Find the measure of the missing angle in the triangle below.

6. What is the sum of the measures of the interior angles of a hexagon?

7. Find the area of the triangle below.

9. Which of the following could be the side lengths of a right triangle?

Therefore, the missing angle is 50°.

## Free Mathematics Tutorials

Free geometry problems and questions writh solutions.

## Geometry Problems

- Triangle Problems . Triangle problems with detailed solutions.
- Congruent Triangles Examples and Problems with Solutions .
- Similar Triangles Examples and Problems with Solutions . Definition and theorems on similar triangles including examples and problems with detailed solutions.
- Equilateral Triangles Problems with Solutions .
- Isosceles Triangles Problems with Solutions .
- Area and Perimeter of Right Triangles Problems With Solution .
- Cosine Law Problems . The cosine law is used to solve word problems.
- Sine Law Problems . The sine law is used to solve word problems.
- Triangle Inscribed in a Circle - Problem With Solution . Inscribed right triangle problem with detailed solution.
- Overlapping Circles Problem . Find overlapping area of two circles: problem with detailed solutions.
- Sectors and Circles Problems . Problems, with detailed solutions, related to sectors and circle.
- Two Squares and a Circle - Problem With Solution . A problem, with detailed solution, on a circle inscribed in one square and circumscribed to another, is presented.

## Quadrilaterals

- Rectangle Problems . Rectangle problems on area, dimensions, perimeter and diagonal with detailed solutions.
- Geometry Problems on Squares . Square problems on area, diagonal and perimeter, with detailed solutions.
- Parallelogram Problems . Word problems related to parallelograms are presented along with detailed solutions.
- Trapezoid Problems . Trapezoid problems are presented along with detailed solutions.
- Solve a Trapezoid Given its Bases and Legs .
- Polygons Problems . Problems related to regular polygons.
- 3D Shapes Volume Problems . 3D shapes, such as prisms, volume problems with detailed solutions.
- Compare Volumes of 3D shapes . A problem to compare the volumes of a cone, a cylinder and a hemisphere.
- How to construct a frustum? . If you cut off the top part of a cone with a plane perpendicular to the height of the cone, you obtain a conical frustum. How to construct a frustum given the radius of the base, the radius of the top and the height?
- Cone Problems . Problems related to the surface area and volume of a cone with detailed solutions are presented.

## Other Geometry Problems

## Geometry Tutorials

- Parts of a Circle .
- Tangents to a Circle with Questions and Solutions .
- Intersecting Secant and Tangent Theorem Questions with Solutions .
- Intersecting Chords Theorem Questions with Solutions.
- Intersecting Secant Theorem Questions with Solutions.
- Semicircle Thales Theorem with questions and solutions
- Triangles . Definitions and properties of triangles in geometry.
- Area of Triangles Problems with Solutions . Use different formulas of the area of a triangle to calculate the areas of triangles and shapes.
- Properties of Triangles . An applet is used to explore,interactively, the properties of triangles.
- Simple Proofs of Pythagorean Theorem and Problems with Solutions .
- Sine law - ambiguous case - applet . The ambiguous case of the sine law, in solving triangle problems, is explored interactively using an applet.
- Altitudes, Medians and Angle Bisectors of a Triangle .
- Quadrilaterals , properties and formulas.
- Angles in Geometry . Definitions and properties of angles in geometry including questions with solutions.
- Angles in Parallel Lines and Transversals . This tutorial is about the corresponding, interior and exterior angles formed when a transversal line intersects two parallel lines.
- Latitude and Longitude Coordinate System .
- Regular Polygons . Tutorial to develop useful formulas for area of regular polygons.

## Other Geometry Topics

- Rotation Symmetry of Geometric Shapes . An interactive tutorial to explore rotation symmetry of geometric shapes.
- Table of Formulas for Geometry . A table of formulas for geometry, related to area and perimeter of triangles, rectangles, circles, sectors, and volume of sphere, cone, cylinder are presented.

## Challenge Geometry Problems

- Two Tangent Circles and a Square - Problem With Solution . You are given the perimeter of a small circle to find the radius of a larger circle inscribed within a square.
- Kite Within a Square - Problem With Solution . A problem on finding the sine of the angle of a kite within a square.
- Solve Triangle Given Its Perimeter, Altitute and Angle - Problem With Solution .
- Solve Right Triangle Given Perimeter and Altitude - Problem With Solution .
- Triangle and Tangent Circle - Problem With Solution . A problem, on a triangle tangent at two points to a circle, is presented along with detailed solution.
- Three Tangent Circles - Problem With Solution . A problem, on three tangent circles, is presented along with solution.
- Equilateral Triangle Within a Square - Problem With Solution . A problem on the proof of an equilateral triangle within a square is presented along with detailed solution.
- Square Inscribed in Right Triangle - Problem With Solution . Find the side of a square inscribed in a right triangle given the sides of the triangle.

## Polar Coordinates

- Plot Points in Polar Coordinates . An interactive tutorial on how to plot points given by their polar coordinates.
- Graphing Polar Equations . This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented.
- Convert Polar to Rectangular Coordinates and Vice Versa . Problems, with detailed solutions, where polar coordinates are converted into rectangular coordinates and vice versa are presented.
- Convert Equation from Rectangular to Polar Form . Problems were equations in rectangular form are converted to polar form, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
- Convert Equation from Polar to Rectangular Form . Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Problems with detailed solutions are presented.

## Geometric Transformations

- Reflection Across a Line . The properties of reflection of shapes across a line are explored using a geometry applet.
- Rotation of Geometric Shapes . The rotations of 2-D shapes are explored.

## Geometric Calculators and Worksheets

- Online Geometry Calculators and Solvers : Several calculators to help in the calculations and solutions of geometry problems.
- Free Geometry Worksheets to Download

## Popular Pages

- 3D Shapes Volume Problems
- Solve Right Triangle Given Perimeter and Area - Problem With Solution
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- Geometry Calculators and Solvers

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The height ( h ) is 6 feet, and the two bases ( b 1 and b 2 ) are 8 and 11 feet.

Adding all three areas gives us a total area of the house of 1,007 square feet.

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## 4.5 Geometric Word Problems

[latex]\text{sum of interior angles} = 180^{\circ} \times (\text{number of sides} - 2)[/latex]

The relationships described in equation form are as follows:

[latex]A_2 = 2A_1 \text{ and } A_3 = A_1 - 40^{\circ}[/latex]

Because the shape in question is a triangle, the interior angles add up to 180°. Therefore:

[latex]A_1 + A_2 + A_3 = 180^{\circ}[/latex]

Which can be simplified using substitutions:

[latex]A_1 + (2A_1) + (A_1 - 40^{\circ}) = 180^{\circ}[/latex]

[latex]L = 2W - 5 \text{ and } P = 44[/latex]

For a rectangle, the perimeter is defined by:

Substituting for [latex]L[/latex] and the value for the perimeter yields:

[latex]44 = 2W + 2 (2W - 5)[/latex]

[latex]44 = 2W + 4W - 10[/latex]

Further simplify to find the length and width:

The width is 9 m and the length is 13 m.

Other common geometric problems are:

[latex]P_1 + P_2 = 15 \text{ and } P_1 = 4P_2[/latex]

This means that [latex]P_2 =[/latex] 3 m and [latex]P_1 = 4 (3),[/latex] or 12 m.

For questions 1 to 8, write the formula defining each relation. Do not solve.

- The length of a rectangle is 3 cm less than double the width, and the perimeter is 54 cm.
- The length of a rectangle is 8 cm less than double its width, and the perimeter is 64 cm.
- The length of a rectangle is 4 cm more than double its width, and the perimeter is 32 cm.
- The first angle of a triangle is twice as large as the second and 10° larger than the third.
- The first angle of a triangle is half as large as the second and 20° larger than the third.
- The sum of the first and second angles of a triangle is half the amount of the third angle.
- A 140 cm cable is cut into two pieces. The first piece is five times as long as the second.
- A 48 m piece of hose is to be cut into two pieces such that the second piece is 5 m longer than the first.

For questions 9 to 18, write and solve the equation describing each relationship.

- The second angle of a triangle is the same size as the first angle. The third angle is 12° larger than the first angle. How large are the angles?
- Two angles of a triangle are the same size. The third angle is 12° smaller than the first angle. Find the measure of the angles.
- Two angles of a triangle are the same size. The third angle is three times as large as the first. How large are the angles?
- The second angle of a triangle is twice as large as the first. The measure of the third angle is 20° greater than the first. How large are the angles?
- Find the dimensions of a rectangle if the perimeter is 150 cm and the length is 15 cm greater than the width.
- If the perimeter of a rectangle is 304 cm and the length is 40 cm longer than the width, find the length and width.
- Find the length and width of a rectangular garden if the perimeter is 152 m and the width is 22 m less than the length.
- If the perimeter of a rectangle is 280 m and the width is 26 m less than the length, find its length and width.
- A lab technician cuts a 12 cm piece of tubing into two pieces such that one piece is two times longer than the other. How long are the pieces?
- An electrician cuts a 30 m piece of cable into two pieces. One piece is 2 m longer than the other. How long are the pieces?

## Share This Book

## Basic Geometry Practice Questions with Full Answer Key – Area, Perimeter, Volume & Angles

## High School geometry questions similar to what you will find on a standardized test.

Most popular geometry questions.

Common geometry questions on on standardized tests :

- Solve for the missing angle or side
- Finding the area or perimeter of different shapes (e.g. triangles, rectangles, circles)
- Problems using the Pythagorean Theorem
- Calculate properties of geometric shapes such as angles, right angles or parallel sides
- Calculating volume or surface area of complex shapes for example spheres, cylinders or cones
- Solve geometric transformations such as rotation, translation or reflections

## Most Common Geometry Mistakes on a Test

- Not clearly labeling or identifying the given and unknown information in a problem
- Not understanding the properties and definitions of basic geometric figures (e.g. line, angle, triangle, etc.)
- Incorrectly using basic formulas (e.g. area of a triangle, Pythagorean theorem)
- Incorrectly interpreting geometric diagrams
- Not understanding the relationship between parallel lines and transversals
- Not understanding the relationship between angles and their degree measures
- Not understanding the relationship between perimeter and area

## Geometry Practice Test

1. What is measurement of the indicated angle assuming the figure is a square?

a. 45 o b. 90 o c. 60 o d. 30 o

2. What is the sum of all the angles in the rectangle above?

a. 180 o b. 360 o c. 90 o d. 120 o

3. What is the measurement of the indicated angle?

a. 45 o b. 90 o c. 60 o d. 50 o

4. If the line m is parallel to the side AB of ? ABC, what is angle a ?

a. 130 o b. 25 o c. 65 o d. 50 o

5. What is perimeter of the above shape?

a. 12 cm b. 16 cm c. 6 cm d. 20 cm

6. What is (area of large circle) – (area of small circle) in the figure above?

a. 8 п cm 2 b. 10 п cm 2 c. 12 п cm 2 d. 16 п cm 2

7. What is perimeter of ? ABC in the above shape?

8. What is the volume of the figure above?

a. 125 cm 3 b. 875 cm 3 c. 1000 cm 3 d. 500 cm 3

a. 1440 п in 3 b. 1260 п in 3 c. 1040 п in 3 d. 960 п in 3

2. B a+b+c+d = ? The sum of angles around a point is 360 o a+b+c+d = 360 o

## Video Solution

3. C The sum of angles around a point is 360 o d+300 = 360 o d = 60 o

4. D Two parallel lines( m & side AB) intersected by side AC a= 50 o (interior angles)

See also our tutorial on Complex Shapes

Tag: Basic Math , Geometry , Practice Questions

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## How to Solve Linear Inequalities – Quick Review and Practice

answer to question five should be 18, you forgot to include the 2cm outer side of the rectangle

Please in no 6 ,42 -22 is 20,so how comes about 16 and how did u get 122 in no 10

In #9, since it is a cylinder; shouldn’t you use Pi in calculating the area of the base??

in question #9 what is the formula of a cylinder if the diameter is given and not the radius?

1) 4*2+2*2 = 12 2) 2(4+2) + 2*2 = 16

Thanks! this was super helpful!

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