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SSAT Upper Level Math : How to find the perimeter of a hexagon

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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:

$1,200\textrm{ mm }$ $\displaystyle 1,200\textrm{ mm }$

$2,000\textrm{ mm }$ $\displaystyle 2,000\textrm{ mm }$

$1,500 \textrm{ mm }$ $\displaystyle 1,500 \textrm{ mm }$

$1,800\textrm{ mm }$ $\displaystyle 1,800\textrm{ mm }$

$2,400 \textrm{ mm }$ $\displaystyle 2,400 \textrm{ mm }$

Correct answer:

$1,500 \textrm{ mm }$ $\displaystyle 1,500 \textrm{ mm }$

Explanation:

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

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

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

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

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

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

Possible Answers:

56-2t $\displaystyle 56-2t$

28+2t $\displaystyle 28+2t$

28-2t $\displaystyle 28-2t$

28-t $\displaystyle 28-t$

56+2t $\displaystyle 56+2t$

Correct answer:

28-2t $\displaystyle 28-2t$

Explanation:

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

$\displaystyle x=$ Length of one of those other two sides

Now we can set up an equation and solve it for $\displaystyle x$ in terms of $\displaystyle t$ :

$\displaystyle 2x+4(t+1)=60$

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

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

$\Rightarrow 2x=56-4t$ $\displaystyle \Rightarrow 2x=56-4t$

$\Rightarrow x=28-2t$ $\displaystyle \Rightarrow x=28-2t$

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

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

Possible Answers:

8t+8 $\displaystyle 8t+8$

6t-6 $\displaystyle 6t-6$

$\displaystyle 6t$

6t+6 $\displaystyle 6t+6$

$\displaystyle 8t$

Correct answer:

$\displaystyle 6t$

Explanation:

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

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

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Example Question #3 : 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:

$\displaystyle 15$

$\displaystyle 30$

$\displaystyle 18$

$\displaystyle 24$

$\displaystyle 36$

Correct answer:

$\displaystyle 30$

Explanation:

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

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

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

$a=2.5\times 12=30$ $\displaystyle a=2.5\times 12=30$ inches

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Example Question #1 : 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:

$60\ inches$ $\displaystyle 60\ inches$

$10\ inches$ $\displaystyle 10\ inches$

$30\ inches$ $\displaystyle 30\ inches$

$25\ inches$ $\displaystyle 25\ inches$

$20\ inches$ $\displaystyle 20\ inches$

Correct answer:

$20\ inches$ $\displaystyle 20\ inches$

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:

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

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

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

Possible Answers:

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 2$

Correct answer:

$\displaystyle 5$

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 $\displaystyle 2t+3$ and the rest of the sides have the length of 2t-7 $\displaystyle 2t-7$ we can write:

$\displaystyle Perimeter=3(2t+3)+3(2t-7)=48$

Now we should solve the equation for $\displaystyle t$ :

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

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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:

$15 \textrm{ in }$ $\displaystyle 15 \textrm{ in }$

$10 \textrm{ in }$ $\displaystyle 10 \textrm{ in }$

$16 \textrm{ in }$ $\displaystyle 16 \textrm{ in }$

$18 \textrm{ in }$ $\displaystyle 18 \textrm{ in }$

$12 \textrm{ in }$ $\displaystyle 12 \textrm{ in }$

Correct answer:

$15 \textrm{ in }$ $\displaystyle 15 \textrm{ in }$

Explanation:

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

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Example Question #5 : Areas And Perimeters Of Polygons

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

Possible Answers:

6a+6b $\displaystyle 6a+6b$

12a+6b $\displaystyle 12a+6b$

36a+6b $\displaystyle 36a+6b$

36a+36b $\displaystyle 36a+36b$

36a+b $\displaystyle 36a+b$

Correct answer:

36a+6b $\displaystyle 36a+6b$

Explanation:

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

P=6s $\displaystyle P=6s$

Substitute the side length.

$\displaystyle P=6s=6(6a+b)=36a+6b$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : How to find the perimeter of a hexagon

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 : How To Find The Perimeter Of A Hexagon

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

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

Example Question #1 : Areas And Perimeters Of Polygons

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

Example Question #6 : Areas And Perimeters Of Polygons

Example Question #5 : Areas And Perimeters Of Polygons

All SSAT Upper Level Math Resources

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