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SSAT Upper Level Math : Area of Polygons

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon with side lengths 12c .

Possible Answers:

$216\sqrt3$

$108c^2\sqrt3$

$216c^2\sqrt3$

$432c^2\sqrt3$

Correct answer:

$216c^2\sqrt3$

Explanation:

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

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times (12c)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 144c^2$

$\text{Area}=\frac{432c^2\sqrt3}{2}=216c^2\sqrt3$

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Example Question #12 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon with side lengths of $\frac{1}{2}$ .

Possible Answers:

$\frac{3\sqrt3}{2}$

$\frac{3\sqrt3}{8}$

$\frac{3\sqrt3}{4}$

$\frac{\sqrt3}{4}$

Correct answer:

$\frac{3\sqrt3}{8}$

Explanation:

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

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times \left(\frac{1}{2}\right)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times \frac{1}{4}$

$\text{Area}=\frac{3\sqrt3}{8}$

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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:

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

$6\sqrt{35\sqrt5}$

$\sqrt{25+10\sqrt5}$

$15+90\sqrt5$

$9\sqrt{10\sqrt5}$

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:

30x^2

120x^2

30x

60x^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

750

1500

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 #11 : Area Of Polygons

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

Possible Answers:

27.53

98.21

41.21

29.11

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:

50z

75z^2

75z

150z

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:

160a^2

120a^2

80a

80a^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:

400b^2

200b^2

300b^2

600b^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 #982 : Ssat Upper Level Quantitative (Math)

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:

22.2

18.2

25.6

20.8

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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SSAT Upper Level Math : Area of Polygons

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #11 : How To Find The Area Of A Hexagon

Example Question #12 : How To Find The Area Of A Hexagon

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 #11 : Area Of Polygons

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 #982 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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