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SSAT Upper Level Math : Areas and Perimeters of Polygons

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

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All SSAT Upper Level Math Resources

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Example Questions

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 #31 : Areas And Perimeters Of Polygons

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:

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

- 6t+ 69

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

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

- 6t+ 39

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 #992 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

$1,400 \textrm{ mm}$

$1,500 \textrm{ mm}$

$2,100 \textrm{ mm}$

$1,800 \textrm{ mm}$

$1,200 \textrm{ mm}$

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

A regular pentagon has perimeter 42 meters. What is the length of one side in centimeters?

Possible Answers:

840

8400

2100

210

Correct answer:

840

Explanation:

One meter is equal to 100 centimeters, so the perimeter of 42 meters can be expressed as follows:

meters $=42\times 100=4200$ centimeters

In a regular pentagon, all sides are equal in length. Divide the perimeter by 5 to get the length of each side:

$4200\div 5=840$ centimeters

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

The perimeter of a pentagon is 4t-4 . The pentagon has three congruent sides of length meters. Its other two sides are congruent to each other, each with a length of .

Find .

Possible Answers:

Correct answer:

Explanation:

The perimeter of a polygon is sum of the lengths of its sides. In this pentagon, three sides have the same length of 4 and two others have the same length of . So we can write:

$Perimeter=4t-4=3\times 4+2\times t$

Now we should solve this equation for :

4t-4=12+2t

4t-2t=12+4

2t=16

t=8

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

A pentagon with perimeter 40 meters has two congruent sides of length 3t+5 . Its other three sides are congruent to each other. Give the length of each of the other three sides in terms of .

Possible Answers:

2t-10

t-5

5-2t

10-2t

5-t

Correct answer:

10-2t

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. Let:

length of one of those other three sides

Now we have:

$Perimeter=40=2\times (3t+5)+3\times x$

40=6t+10+3x

40-10-6t=3x

30-6t=3x

10-2t=x

So the length of each of those other three sides is 10-2t

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Example Question #4 : How To Find The Perimeter Of A Pentagon

Two sides of a pentagon have a length of t-1 , and three other sides have the length of t+1 . Give the perimeter of the pentagon in terms of .

Possible Answers:

5t+1

5t+2

5t-1

10t+1

10t-1

Correct answer:

5t+1

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. So we can write:

$Perimeter=2\times (t-1)+ 3\times (t+1)$

=2t-2+3t+3

=5t+1

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

Each exterior angle of a pentagon is 72 degrees and the length of one side is 4 meters. Give the perimeter of the pentagon.

Possible Answers:

Correct answer:

Explanation:

As each exterior angle of the pentagon is 72 degrees, each interior angle would be

$180-72=108^{\circ}$

That means all of the interior angles of the pentagon are identical, so we have a regular pentagon.

The perimeter of a polygon is the sum of the lengths of its sides. So the perimeter of a regular pentagon is ; where is the length of a side.

So we get:

$Perimeter=5a=5\times 4=20$ meters

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SSAT Upper Level Math : Areas and Perimeters of Polygons

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

All SSAT Upper Level Math Resources

Example Questions

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 #31 : Areas And Perimeters Of Polygons

Example Question #992 : Ssat Upper Level Quantitative (Math)

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

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

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

Example Question #4 : How To Find The Perimeter Of A Pentagon

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

All SSAT Upper Level Math Resources

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