HSPT Math : How to find the area of a figure

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #257 : Geometric Measurement: Understanding Concepts Of Area And Relating Area To Multiplication And To Addition

What is the area of the figure below?


5

Possible Answers:

\(\displaystyle 36in^2\)

\(\displaystyle 72in^2\)

\(\displaystyle 49in^2\)

\(\displaystyle 52in^2\)

\(\displaystyle 68in^2\)

Correct answer:

\(\displaystyle 52in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

5.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=4\times 4\)            \(\displaystyle A=12\times 3\)

\(\displaystyle A=16in^2\)           \(\displaystyle A=36in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 16in^2+36in^2=52in^2\)

Example Question #31 : How To Find The Area Of A Figure

What is the area of the figure below?


4

Possible Answers:

\(\displaystyle 93in^2\)

\(\displaystyle 89in^2\)

\(\displaystyle 49in^2\)

\(\displaystyle 35in^2\)

\(\displaystyle 54in^2\)

Correct answer:

\(\displaystyle 89in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

4.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=9\times 6\)            \(\displaystyle A=7\times 5\)

\(\displaystyle A=54in^2\)           \(\displaystyle A=35in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 54in^2+35in^2=89in^2\)

Example Question #131 : Plane Geometry

What is the area of the figure below?

3

Possible Answers:

\(\displaystyle 33in^2\)

\(\displaystyle 50in^2\)

\(\displaystyle 42in^2\)

\(\displaystyle 72in^2\)

\(\displaystyle 63in^2\)

Correct answer:

\(\displaystyle 42in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

3.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=11\times 3\)            \(\displaystyle A=3\times 3\)

\(\displaystyle A=33in^2\)           \(\displaystyle A=9in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 33in^2+9in^2=42in^2\)

Example Question #132 : Plane Geometry

What is the area of the figure below?

1

Possible Answers:

\(\displaystyle 31in^2\)

\(\displaystyle 15in^2\)

\(\displaystyle 30in^2\)

\(\displaystyle 21in^2\)

\(\displaystyle 10in^2\)

Correct answer:

\(\displaystyle 31in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

1.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=7\times 3\)            \(\displaystyle A=5\times 2\)

\(\displaystyle A=21in^2\)           \(\displaystyle A=10in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 21in^2+10in^2=31in^2\)

Example Question #133 : Plane Geometry

What is the area of the figure below?

2

Possible Answers:

\(\displaystyle 10in^2\)

\(\displaystyle 22in^2\)

\(\displaystyle 6in^2\)

\(\displaystyle 8in^2\)

\(\displaystyle 16in^2\)

Correct answer:

\(\displaystyle 22in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

2.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=4\times 4\)            \(\displaystyle A=3\times 2\)

\(\displaystyle A=16in^2\)           \(\displaystyle A=6in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 16in^2+6in^2=22in^2\)

Example Question #134 : Plane Geometry

What is the area of the figure below?

12

Possible Answers:

\(\displaystyle 52in^2\)

\(\displaystyle 84in^2\)

\(\displaystyle 48in^2\)

\(\displaystyle 111in^2\)

\(\displaystyle 63in^2\)

Correct answer:

\(\displaystyle 111in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

12.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=7\times 9\)            \(\displaystyle A=8\times 6\)

\(\displaystyle A=63in^2\)           \(\displaystyle A=48in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 63in^2+48in^2=111in^2\)

Example Question #241 : Problem Solving

What is the area of the figure below?

11

Possible Answers:

\(\displaystyle 84in^2\)

\(\displaystyle 72in^2\)

\(\displaystyle 60in^2\)

\(\displaystyle 32in^2\)

\(\displaystyle 28in^2\)

Correct answer:

\(\displaystyle 60in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

11.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=8\times 4\)            \(\displaystyle A=7\times 4\)

\(\displaystyle A=32in^2\)           \(\displaystyle A=28in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 32in^2+28in^2=60in^2\)

Example Question #136 : Plane Geometry

What is the area of the figure below?

10

Possible Answers:

\(\displaystyle 38in^2\)

\(\displaystyle 40in^2\)

\(\displaystyle 76in^2\)

\(\displaystyle 81in^2\)

\(\displaystyle 36in^2\)

Correct answer:

\(\displaystyle 76in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

10.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=9\times 4\)            \(\displaystyle A=8\times 5\)

\(\displaystyle A=36in^2\)           \(\displaystyle A=40in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 36in^2+40in^2=76in^2\)

Example Question #137 : Plane Geometry

What is the area of the figure below?

9

Possible Answers:

\(\displaystyle 75in^2\)

\(\displaystyle 110in^2\)

\(\displaystyle 50in^2\)

\(\displaystyle 160in^2\)

\(\displaystyle 93in^2\)

Correct answer:

\(\displaystyle 160in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

9.5

Using our area formula, \(\displaystyle A=l\times w\), we can solve for the area of both of our rectangles

\(\displaystyle A=11\times 10\)            \(\displaystyle A=10\times 5\)

\(\displaystyle A=110in^2\)           \(\displaystyle A=50in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 110in^2+50in^2160in^2\)

Example Question #31 : How To Find The Area Of A Figure

What is the area of the figure below?


8

Possible Answers:

\(\displaystyle 24in^2\)

\(\displaystyle 72in^2\)

\(\displaystyle 50in^2\)

\(\displaystyle 84in^2\)

\(\displaystyle 48in^2\)

Correct answer:

\(\displaystyle 72in^2\)

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles. 

 

8.5

\(\displaystyle A=8\times 6\)            \(\displaystyle A=6\times 4\)

\(\displaystyle A=48in^2\)           \(\displaystyle A=24in^2\)

To find our final answer, we need to add the areas together. 

\(\displaystyle 48in^2+24in^2=72in^2\)

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