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 #281 : Plane Geometry

What is the area of the figure below?


7

Possible Answers:

\(\displaystyle 37in^2\)

\(\displaystyle 49in^2\)

\(\displaystyle 74in^2\)

\(\displaystyle 63in^2\)

\(\displaystyle 25in^2\)

Correct answer:

\(\displaystyle 74in^2\)

Explanation:

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

7.5

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

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

\(\displaystyle A=49in^2\)           \(\displaystyle A=25in^2\)

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

\(\displaystyle 49in^2+25in^2=74in^2\)

Example Question #51 : Rectangles

What is the area of the figure below?

6

Possible Answers:

\(\displaystyle 132in^2\)

\(\displaystyle 84in^2\)

\(\displaystyle 119in^2\)

\(\displaystyle 35in^2\)

\(\displaystyle 127in^2\)

Correct answer:

\(\displaystyle 119in^2\)

Explanation:

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

6.5

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

\(\displaystyle A=7\times 12\)            \(\displaystyle A=7\times 5\)

\(\displaystyle A=84in^2\)           \(\displaystyle A=35in^2\)

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

\(\displaystyle 84in^2+35in^2=119in^2\)

Example Question #52 : Rectangles

What is the area of the figure below?


5

Possible Answers:

\(\displaystyle 46in^2\)

\(\displaystyle 77in^2\)

\(\displaystyle 55in^2\)

\(\displaystyle 25in^2\)

\(\displaystyle 37in^2\)

Correct answer:

\(\displaystyle 77in^2\)

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

\(\displaystyle A=5\times 5\)            \(\displaystyle A=13\times 4\)

\(\displaystyle A=25in^2\)           \(\displaystyle A=52in^2\)

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

\(\displaystyle 25in^2+52in^2=77in^2\)

Example Question #41 : How To Find The Area Of A Figure

What is the area of the figure below?


4

Possible Answers:

\(\displaystyle 132in^2\)

\(\displaystyle 40in^2\)

\(\displaystyle 118in^2\)

\(\displaystyle 48in^2\)

\(\displaystyle 70in^2\)

Correct answer:

\(\displaystyle 118in^2\)

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

\(\displaystyle A=10\times 7\)            \(\displaystyle A=6\times 8\)

\(\displaystyle A=70in^2\)           \(\displaystyle A=48in^2\)

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

\(\displaystyle 70in^2+48in^2=118in^2\)

Example Question #31 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

3

Possible Answers:

\(\displaystyle 28in^2\)

\(\displaystyle 58in^2\)

\(\displaystyle 16in^2\)

\(\displaystyle 48in^2\)

\(\displaystyle 64in^2\)

Correct answer:

\(\displaystyle 64in^2\)

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

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

\(\displaystyle A=48in^2\)           \(\displaystyle A=16in^2\)

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

\(\displaystyle 48in^2+16in^2=64in^2\)

Example Question #32 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

1

Possible Answers:

\(\displaystyle 18in^2\)

\(\displaystyle 50in^2\)

\(\displaystyle 64in^2\)

\(\displaystyle 32in^2\)

\(\displaystyle 72in^2\)

Correct answer:

\(\displaystyle 50in^2\)

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

\(\displaystyle A=4\times 8\)            \(\displaystyle A=3\times 6\)

\(\displaystyle A=32in^2\)           \(\displaystyle A=18in^2\)

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

\(\displaystyle 32in^2+18in^2=50in^2\)

Example Question #33 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

2

Possible Answers:

\(\displaystyle 25in^2\)

\(\displaystyle 51in^2\)

\(\displaystyle 57in^2\)

\(\displaystyle 43in^2\)

\(\displaystyle 37in^2\)

Correct answer:

\(\displaystyle 37in^2\)

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

\(\displaystyle A=5\times 5\)            \(\displaystyle A=4\times 3\)

\(\displaystyle A=25in^2\)           \(\displaystyle A=12in^2\)

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

\(\displaystyle 25in^2+12in^2=37in^2\)

Example Question #41 : How To Find The Area Of A Figure

What is the area of a triangle with a side lengths of 5?

Possible Answers:

\(\displaystyle 5\)

Cannot be determined

\(\displaystyle 12.5\)

\(\displaystyle 25\)

\(\displaystyle 125\)

Correct answer:

Cannot be determined

Explanation:

The area of a triangle is found with the equation 

\(\displaystyle a=\frac{1}{2}b h\).  

Since we do not have the height, we cannot answer the question. 

Example Question #42 : How To Find The Area Of A Figure

What is the area of a triangle with a base of 22 cm and a height of 9 cm? 

Possible Answers:

\(\displaystyle 198\ cm^{2}\)

\(\displaystyle 98\ cm^{2}\)

\(\displaystyle 99\ cm^{2}\)

\(\displaystyle 45\ cm^{2}\)

Correct answer:

\(\displaystyle 99\ cm^{2}\)

Explanation:

Use the area of a triangle formula

\(\displaystyle A=\frac{1}{2}bh\)

Plug in the base and height. This gives you \(\displaystyle 99\ cm^{2}\).

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