# Polygon

• Sep 23rd 2013, 10:56 PM
Polygon
What is the perimeter, in units, of a regular 11-sided polygon with sides of length .36363636… units?

I don't know how to find the answer to this problem. Please use words that a 7th grader can understand. Thanks!
• Sep 23rd 2013, 11:35 PM
votan
Re: Polygon
The perimeter is the sum of all the sides of a figure. For instance, the perimeter of a triangle is the sum of the lengths of the three sides. the perimeter of a rectangle is the sum of the length of the four sides. Can you now find the perimeter of your polygon.
• Sep 24th 2013, 05:40 AM
Prove It
Re: Polygon
Quote:

What is the perimeter, in units, of a regular 11-sided polygon with sides of length .36363636… units?

I don't know how to find the answer to this problem. Please use words that a 7th grader can understand. Thanks!

First of all, it would help if you wrote the length of each side as a fraction, as they are exact.

\displaystyle \begin{align*} x &= 0.363636\dots \\ 100x &= 36.363636\dots \\ 100x - x &= 36.363636\dots - 0.363636\dots \\ 99x &= 36 \\ x &= \frac{36}{99} \\ x &= \frac{4}{11} \end{align*}

So that means each side is \displaystyle \begin{align*} \frac{4}{11} \end{align*} of a unit in length, and since there are 11 sides, the perimeter is \displaystyle \begin{align*} 11 \times \frac{4}{11} = 4 \end{align*} units.
• Sep 24th 2013, 08:48 PM
\displaystyle \begin{align*} x &= 0.363636\dots \\ 100x &= 36.363636\dots \\ 100x - x &= 36.363636\dots - 0.363636\dots \\ 99x &= 36 \\ x &= \frac{36}{99} \\ x &= \frac{4}{11} \end{align*}
So that means each side is \displaystyle \begin{align*} \frac{4}{11} \end{align*} of a unit in length, and since there are 11 sides, the perimeter is \displaystyle \begin{align*} 11 \times \frac{4}{11} = 4 \end{align*} units.