The Length of the Sides of Polygons

Date: 3/7/96 at 15:52:12
From: Sweet Home Middle School
Subject: pentagons, octagons, polygons

Dear Dr. Math:

Our 7th grade math students have more geometry questions for you:

How many feet should each side be in a regular octagon if the area is 
7,000 square feet? - Christy, Jennifer, Mike, and Chris

How many feet should each side be in a regular hexagon if the area
is 7,000 square feet? - Steve, Collin, Matty, Rob, and Paul

How many feet should each side be in a regular pentagon if the area
is 7,000 square feet?  Does the 7,000 ft. count for in the middle?  Joe 
G., Tim J, Anthony D.

Thanks in advance for your prompt reply.

Mrs. Reimer's 5th period math class
Sweet Home Middle School
Amherst, N.Y. 14226

Date: 3/20/96 at 11:19:16
From: Doctor Ken
Subject: Re: pentagons, octagons, polygons

Hello!

Here's a hint on how to do these problems.  

If we had a formula for the area of a regular octagon in terms of the 
side length, this would be easier, right?  

For example, we have a formula like that for a regular (equilateral) 
triangle: if s is the side length, then   

Area = s^2 * Sqrt{3}/4.  (do you know why?)

So if we wanted to find the side length for an equilateral triangle that 
had an area of 7000 square feet, we'd solve the equation 
7000 = s^2 * Sqrt{3}/4, and we'd find that s is about 127.

To find these formulas in the first place, you have to use geometry, 
and maybe even a little trigonometry.  The hexagon is the easiest; 
you might want to start with that one.

Good luck!

-Doctor Ken,  The Math Forum