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ISEE Upper Level Math : How to find the length of the side of a hexagon

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Example Questions

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

What is the sidelength, in feet and inches, of a regular hexagon with perimeter 16 feet?

Possible Answers:

$1 \textrm{ ft }4 \textrm{ in}$ $\displaystyle 1 \textrm{ ft }4 \textrm{ in}$

$3 \textrm{ ft }2 \frac{2}{5} \textrm{ in}$ $\displaystyle 3 \textrm{ ft }2 \frac{2}{5} \textrm{ in}$

$2 \textrm{ ft }$ $\displaystyle 2 \textrm{ ft }$

$1 \textrm{ ft }7 \frac{1}{5} \textrm{ in}$ $\displaystyle 1 \textrm{ ft }7 \frac{1}{5} \textrm{ in}$

$2 \textrm{ ft }8 \textrm{ in}$ $\displaystyle 2 \textrm{ ft }8 \textrm{ in}$

Correct answer:

$2 \textrm{ ft }8 \textrm{ in}$ $\displaystyle 2 \textrm{ ft }8 \textrm{ in}$

Explanation:

Divide the perimeter 16 feet by 6 to get the sidelength of the hexagon in feet:

$16 \div 6 = 2\frac{2}{3} \textrm{ ft }$ $\displaystyle 16 \div 6 = 2\frac{2}{3} \textrm{ ft }$

Two-thirds of a foot is equal to eight inches, so this sidelength is 2 feet 8 inches.

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

The perimeter of a regular hexagon is one mile. Give the sidelength in feet.

Possible Answers:

$660 \textrm{ ft}$ $\displaystyle 660 \textrm{ ft}$

$1,320 \textrm{ ft}$ $\displaystyle 1,320 \textrm{ ft}$

$880 \textrm{ ft}$ $\displaystyle 880 \textrm{ ft}$

$330 \textrm{ ft}$ $\displaystyle 330 \textrm{ ft}$

$990 \textrm{ ft}$ $\displaystyle 990 \textrm{ ft}$

Correct answer:

$880 \textrm{ ft}$ $\displaystyle 880 \textrm{ ft}$

Explanation:

One mile is equal to 5,280 feet, so divide this by 6:

$5,280 \div 6 = 880$ $\displaystyle 5,280 \div 6 = 880$ feet

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Example Question #2 : Hexagons

A hexagon has a perimeter of 114in. Find the length of one side.

Possible Answers:

$20\text{in}$ $\displaystyle 20\text{in}$

$22\text{in}$ $\displaystyle 22\text{in}$

$17\text{in}$ $\displaystyle 17\text{in}$

$19\text{in}$ $\displaystyle 19\text{in}$

$12\text{in}$ $\displaystyle 12\text{in}$

Correct answer:

$19\text{in}$ $\displaystyle 19\text{in}$

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

P = 6a $\displaystyle P = 6a$

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 114in. So, we will substitute and solve for a. We get

$114\text{in} = 6a$ $\displaystyle 114\text{in} = 6a$

$\frac{114\text{in}}{6} = \frac{6a}{6}$ $\displaystyle \frac{114\text{in}}{6} = \frac{6a}{6}$

$19\text{in} = a$ $\displaystyle 19\text{in} = a$

$a = 19\text{in}$ $\displaystyle a = 19\text{in}$

Therefore, the length of one side of the hexagon is 19in.

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Example Question #1 : Hexagons

The perimeter of a hexagon is 96cm. Find the length of one side.

Possible Answers:

$13\text{cm}$ $\displaystyle 13\text{cm}$

$16\text{cm}$ $\displaystyle 16\text{cm}$

$14\text{cm}$ $\displaystyle 14\text{cm}$

$19\text{cm}$ $\displaystyle 19\text{cm}$

$18\text{cm}$ $\displaystyle 18\text{cm}$

Correct answer:

$16\text{cm}$ $\displaystyle 16\text{cm}$

Explanation:

A hexagon has 6 equal sides. To find the length of one side of a hexagon, we will use the formula to find the perimeter.

P = 6a $\displaystyle P = 6a$

where a is the length of one side. So, we will solve for a.

Now, we know the perimeter of the hexagon is 96cm. So, we get

$96\text{cm} = 6a$ $\displaystyle 96\text{cm} = 6a$

$\frac{96\text{cm}}{6} = \frac{6a}{6}$ $\displaystyle \frac{96\text{cm}}{6} = \frac{6a}{6}$

$16\text{cm} = a$ $\displaystyle 16\text{cm} = a$

$a = 16\text{cm}$ $\displaystyle a = 16\text{cm}$

Therefore, the length of one side of the hexagon is 16cm.

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ISEE Upper Level Math : How to find the length of the side of a hexagon

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

All ISEE Upper Level Math Resources

Example Questions

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

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

Example Question #2 : Hexagons

Example Question #1 : Hexagons

All ISEE Upper Level Math Resources

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