The Length of the Sides of PolygonsDate: 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 |
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