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SSAT Upper Level Math : Perimeter of Polygons

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Example Questions

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

A regular hexagon has perimeter 9 meters. Give the length of one side in millimeters.

Possible Answers:

$1,800\textrm{ mm }$

$2,000\textrm{ mm }$

$1,200\textrm{ mm }$

$1,500 \textrm{ mm }$

$2,400 \textrm{ mm }$

Correct answer:

$1,500 \textrm{ mm }$

Explanation:

One meter is equal to 1,000 millimeters, so the perimeter of 9 meters can be expressed as:

9 meters = $9 \times 1,000 = 9,000$ millimeters.

Since the six sides of a regular hexagon are congruent, divide by 6:

$9,000 \div 6 = 1,500$ millimeters.

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Example Question #1 : Perimeter Of Polygons

A hexagon with perimeter 60 has four congruent sides of length t+1 . Its other two sides are congruent to each other. Give the length of each of those other sides in terms of .

Possible Answers:

28-2t

28+2t

56-2t

56+2t

28-t

Correct answer:

28-2t

Explanation:

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

Length of one of those other two sides

Now we can set up an equation and solve it for in terms of :

2x+4(t+1)=60

$\Rightarrow 2x+4t+4=60$

$\Rightarrow 2x=60-4-4t$

$\Rightarrow 2x=56-4t$

$\Rightarrow x=28-2t$

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

Two sides of a hexagon have a length of , two other sides have the length of t-1 , and the rest of the sides have the length of t+1 . Give the perimeter of the hexagon.

Possible Answers:

6t+6

6t-6

8t+8

Correct answer:

Explanation:

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

$Perimeter=2\left [ t+(t+1)+(t-1) \right ]=2(3t)=6t$

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

A regular hexagon has perimeter 15 feet. Give the length of one side in inches.

Possible Answers:

Correct answer:

Explanation:

As the six sides of a regular hexagon are congruent, we can write:

$Perimeter=6a=15\Rightarrow a=2.5$ feet; is the length of each side.

One feet is equal to 12 inches, so we can write:

$a=2.5\times 12=30$ inches

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

Each interior angle of a hexagon is 120 degrees and the perimeter of the hexagon is 120 inches. Find the length of each side of the hexagon.

Possible Answers:

$20\ inches$

$60\ inches$

$30\ inches$

$25\ inches$

$10\ inches$

Correct answer:

$20\ inches$

Explanation:

Since each interior angle of a hexagon is 120 degrees, we have a regular hexagon with identical side lengths. And we know that the perimeter of a polygon is the sum of the lengths of its sides. So we can write:

$Perimeter=6a=120\Rightarrow a=20$ inches

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Example Question #3 : Perimeter Of Polygons

A hexagon with perimeter of 48 has three congruent sides of 2t+3 . Its other three sides are congruent to each other with the length of 2t-7 . Find .

Possible Answers:

Correct answer:

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. Since three sides are congruent with the length of 2t+3 and the rest of the sides have the length of 2t-7 we can write:

Perimeter=3(2t+3)+3(2t-7)=48

Now we should solve the equation for :

$6t+9+6t-21=48\Rightarrow 12t-12=48\Rightarrow 12t=60\Rightarrow t=5$

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Example Question #741 : Geometry

A regular pentagon has sidelength one foot; a regular hexagon has sidelength ten inches. The perimeter of a regular octagon is the sum of the perimeters of the pentagon and the hexagon. What is the measure of one side of the octagon?

Possible Answers:

$18 \textrm{ in }$

$15 \textrm{ in }$

$12 \textrm{ in }$

$16 \textrm{ in }$

$10 \textrm{ in }$

Correct answer:

$15 \textrm{ in }$

Explanation:

A regular polygon has all of its sides the same length. The pentagon has perimeter $5 \times 12 \textrm{ in } = 60 \textrm{ in }$ ; the hexagon has perimeter $6 \times 10 \textrm{ in } = 60 \textrm{ in }$ . The sum of the perimeters is $60 \textrm{ in } + 60 \textrm{ in }= 120 \textrm{ in }$ , which is the perimeter of the octagon; each side of the octagon has length $120 \textrm{ in } \div 8 = 15 \textrm{ in }$ .

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Example Question #6 : How To Find The Perimeter Of A Hexagon

Find the perimeter of a hexagon with a side length of 6a+b .

Possible Answers:

36a+b

12a+6b

6a+6b

36a+6b

36a+36b

Correct answer:

36a+6b

Explanation:

A hexagon has six sides. The perimeter of a hexagon is:

P=6s

Substitute the side length.

P=6s=6(6a+b)=36a+6b

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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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SSAT Upper Level Math : Perimeter of Polygons

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 Perimeter Of A Hexagon

Example Question #1 : Perimeter Of Polygons

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

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

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

Example Question #3 : Perimeter Of Polygons

Example Question #741 : Geometry

Example Question #6 : How To Find The Perimeter Of A Hexagon

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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