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 #135 : Plane Geometry

What is the area of the figure below?

11

Possible Answers:

\displaystyle 84in^2

\displaystyle 60in^2

\displaystyle 72in^2

\displaystyle 28in^2

\displaystyle 32in^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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