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SSAT Upper Level Math : Areas and Perimeters of Polygons

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Example Questions

Example Question #1 : Areas And Perimeters Of Polygons

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

Possible Answers:

$1,200\textrm{ mm }$

$1,800\textrm{ mm }$

$2,000\textrm{ mm }$

$1,500 \textrm{ mm }$

$2,400 \textrm{ mm }$

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 : Areas And Perimeters 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-t

56+2t

28-2t

56-2t

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 #1 : Areas And Perimeters Of Polygons

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 : Areas And Perimeters Of Polygons

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 #5 : Areas And Perimeters Of Polygons

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:

$30\ inches$

$20\ inches$

$10\ inches$

$60\ inches$

$25\ inches$

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 #2 : 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 #6 : Areas And Perimeters Of Polygons

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:

$15 \textrm{ in }$

$10 \textrm{ in }$

$16 \textrm{ in }$

$18 \textrm{ in }$

$12 \textrm{ in }$

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 #7 : 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

36a+6b

36a+36b

12a+6b

6a+6b

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 Area Of A Hexagon

Find the area of a regular hexagon that has side lengths of .

Possible Answers:

$36\sqrt3$

$48\sqrt3$

$54\sqrt3$

Correct answer:

$54\sqrt3$

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.

$\text{Area}=\frac{3\sqrt3}{2}\times6^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 36$

$\text{Area}=\frac{108\sqrt3}{2}=54\sqrt3$

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

Find the area of a regular hexagon that has a side length of .

Possible Answers:

192

$48\sqrt3$

$192\sqrt3$

$96\sqrt3$

Correct answer:

$96\sqrt3$

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.

$\text{Area}=\frac{3\sqrt3}{2}\times 8^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 64$

$\text{Area}=\frac{192\sqrt3}{2}=96\sqrt3$

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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 #1 : Areas And Perimeters Of Polygons

Example Question #1 : Areas And Perimeters Of Polygons

Example Question #1 : Areas And Perimeters Of Polygons

Example Question #4 : Areas And Perimeters Of Polygons

Example Question #5 : Areas And Perimeters Of Polygons

Example Question #2 : Perimeter Of Polygons

Example Question #6 : Areas And Perimeters Of Polygons

Example Question #7 : How To Find The Perimeter Of A Hexagon

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

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

All SSAT Upper Level Math Resources

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