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SSAT Upper Level Math : How to find the area of a pentagon

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : How To Find The Area Of A Pentagon

Find the exact area of a pentagon if the side length is .

Possible Answers:

$6\sqrt{35\sqrt5}$

$15+90\sqrt5$

$9\sqrt{10\sqrt5}$

$\sqrt{25+10\sqrt5}$

$9\sqrt{25+10\sqrt5}$

Correct answer:

$9\sqrt{25+10\sqrt5}$

Explanation:

Write the formula for the area of a pentagon.

$A=\frac{s^{2}}{4}\sqrt{5(5+2\sqrt5)}$

Substitute the side length and simplify.

$A=\frac{6^{2}}{4}\sqrt{5(5+2\sqrt5)}$

$A= 9\sqrt{25+10\sqrt5}$

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Example Question #2 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

60x^2

30x^2

30x

120x^2

Correct answer:

30x^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 6x=30x$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(30x)(2x)=30x^2$

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Example Question #3 : How To Find The Area Of A Pentagon

Find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

2000

500

1500

750

Correct answer:

750

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times20=100$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(100)(15)=750$

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Example Question #1 : How To Find The Area Of A Pentagon

Find the area of a regular pentagon with a side length of .

Possible Answers:

41.21

29.11

27.53

98.21

Correct answer:

27.53

Explanation:

Use the following formula to find the area of a regular pentagon:

$\text{Area}=\frac{1}{4}\sqrt{5(5+2\sqrt5)}(side)^2$

Plugging in the information given by the question,

$\text{Area}=\frac{1}{4}\sqrt{5(5+2\sqrt5)}(4)^2=27.53$

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Example Question #5 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of and an apothem of .

Possible Answers:

150z

50z

75z^2

75z

Correct answer:

75z

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 5z =25z$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(25z)(6)=75z$

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Example Question #6 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

80a

80a^2

120a^2

160a^2

Correct answer:

80a^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 8a=40a$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(40a)(4a)=80a^2$

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Example Question #7 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of 12b and an apothem of 10b .

Possible Answers:

600b^2

200b^2

300b^2

400b^2

Correct answer:

300b^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 12b=60b$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60b)(10b)=300b^2$

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Example Question #8 : How To Find The Area Of A Pentagon

The area of a regular polygon is 512 . If the length of its apothem is , what is the length of each side of the pentagon?

Possible Answers:

18.2

20.8

22.2

25.6

Correct answer:

25.6

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$512=\frac{1}{2}(Perimeter)(8)$

8(Perimeter)=1024

Perimeter=128

To find the length of each side of the pentagon, divide the perimeter by .

Side=25.6

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Example Question #9 : How To Find The Area Of A Pentagon

A regular pentagon has an area of 250 . Find the length of each side of the pentagon if the apothem has a length of .

Possible Answers:

Correct answer:

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$250=\frac{1}{2}(Perimeter)(5)$

5(Perimeter)=500

Perimeter=100

To find the length of each side of the pentagon, divide the perimeter by .

Side=20

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Example Question #1 : How To Find The Area Of A Pentagon

The area of a regular pentagon is 410 . Find the length of a side of the pentagon if the apothem has a length of .

Possible Answers:

$\frac{41}{3}$

$\frac{15}{2}$

$\frac{61}{3}$

Correct answer:

$\frac{41}{3}$

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$410=\frac{1}{2}(Perimeter)(12)$

12(Perimeter)=820

$Perimeter=\frac{820}{12}$

To find the length of each side of the pentagon, divide the perimeter by .

$Side=\frac{820}{60}=\frac{41}{3}$

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SSAT Upper Level Math : How to find the area of a pentagon

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Pentagon

Example Question #2 : How To Find The Area Of A Pentagon

Example Question #3 : How To Find The Area Of A Pentagon

Example Question #1 : How To Find The Area Of A Pentagon

Example Question #5 : How To Find The Area Of A Pentagon

Example Question #6 : How To Find The Area Of A Pentagon

Example Question #7 : How To Find The Area Of A Pentagon

Example Question #8 : How To Find The Area Of A Pentagon

Example Question #9 : How To Find The Area Of A Pentagon

Example Question #1 : How To Find The Area Of A Pentagon

All SSAT Upper Level Math Resources

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