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SSAT Upper Level Math : Geometry

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 #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 #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:

20.8

22.2

18.2

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 #1 : 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 #10 : 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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Example Question #982 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

120

180

Correct answer:

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,

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

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60)(3)=90$

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Example Question #983 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

Correct answer:

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,

$\text{Perimeter}=5\times6=30$

So then, to find the area of the pentagon,

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

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

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

Possible Answers:

180

120

240

Correct answer:

120

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,

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

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60)(4)=120$

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

A pentagon with perimeter 54 has three congruent sides of length 2t-5 ; its other two sides are congruent to each other. Give the length of each of those other two sides in terms of .

Possible Answers:

$\frac{- 6t+ 39 }{2}$

$\frac{- 6t+ 59 }{2}$

- 6t+ 69

- 6t+ 39

$\frac{- 6t+ 69 }{2}$

Correct answer:

$\frac{- 6t+ 69 }{2}$

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. If we let be the length of one of those other two sides, we can set up this equation and solve for :

2X + 3 (2t-5) = 54

$2X + 3 \cdot 2t-3 \cdot 5 = 54$

2X +6t-15 = 54

2X +6t-15 + 15 - 6t= 54+ 15 - 6t

2X =69- 6t

$2X \div 2 =\left ( 69- 6t \right )\div 2$

$X =\frac{- 6t+ 69 }{2}$

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

A regular pentagon has perimeter 7 meters. Give the length of one side in millimeters.

Possible Answers:

$1,500 \textrm{ mm}$

$1,400 \textrm{ mm}$

$1,800 \textrm{ mm}$

$2,100 \textrm{ mm}$

$1,200 \textrm{ mm}$

Correct answer:

$1,400 \textrm{ mm}$

Explanation:

One meter is equal to 1,000 millimeters, so the perimeter of 7 meters can be expressed as:

7 meters = $7 \times 1,000 = 7,000$ millimeters.

Since the five sides of a regular pentagon are congruent, divide by 5:

$7,000 \div 5 = 1,400$ millimeters.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

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 #1 : How To Find The Area Of A Pentagon

Example Question #10 : How To Find The Area Of A Pentagon

Example Question #982 : Ssat Upper Level Quantitative (Math)

Example Question #983 : Ssat Upper Level Quantitative (Math)

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

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

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

All SSAT Upper Level Math Resources

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