How to find the length of a side in other polygons

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ISEE Upper Level Quantitative Reasoning › How to find the length of a side in other polygons

Questions 1 - 3

1

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

$9 \textrm{ ft } 7\frac{ 1}{2} \textrm{ in }$

$12 \textrm{ ft } 10 \textrm{ in }$

$7\textrm{ ft } 8 \frac{2}{5} \textrm{ in }$

$11\textrm{ ft } 8 \textrm{ in }$

$7\textup{ ft } 11 \textrm{ in}$

Explanation

feet is equivalent to $77 \times 12 = 924$ inches. Each side of a regular octagon, an eight-sided figure, measures one-eighth of this:

Each side of an octagon with perimeter feet measures

$924 \div 8 = 115\frac{1}{2}$ inches.

Since

$115\frac{1}{2} \div 12 = 9 \textrm{ R } 7 \frac{1}{2}$ ,

this is equal to $9 \textrm{ ft } 7\frac{ 1}{2} \textrm{ in }$ .

2

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

$660 \textrm{ ft}$

$330 \textrm{ ft}$

$1,320 \textrm{ ft}$

$990 \textrm{ ft}$

$880 \textrm{ ft}$

Explanation

One mile is equal to 5,280 feet, so divide this by 8:

$5,280 \div 8 = 660$ feet

3

In a septagon, each of the sides are equal to one another. If the perimeter is feet, what is the length of one of the sides?

Explanation

If the perimeter of a septagon, in which each side is equal to the other, is 98, the length of each side will be 7 feet because 98 divided by 7 is 14.

$P=7\cdot s$

$98=7\cdot s$

$\frac{98}{7}=s$

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