## octoberchick1011 3 years ago The area of a regular hexagon is 35 in^2. What is the length of one side.

1. mishy297

A regular hexagon is made up of 6 trangles with vertex angles of 60 degrees. Each triangle will have an area of 35/6 in^2 and will be equilateral. Each of those triangles can be split into two right triangles. The angles of those right triangles would be 30, 60, 90 degrees and the areas of theses right triangles would be 35/12 in^2 which equals 0.5 *base* height. For a right triangle made out of an equilateral triangle, the base would be 1/2 the hypotnuse. Therefore the equation for the right triangle would be hyp^2 = b^2 + h^2. Substituting that we know we can right it as follows: 2(b)^2= b^2= (70/12b)^2 where h (the height)= (35/12) *2/b=70/12b 4b^2=b^2= (4900/144b^2) since b =0.5s S^2= S^4/4 + (4900/36) (3/4)S^4= 4900/36 S^4= 19600/108= 181.5 s=3.7 inches

2. mishy297

Sorry for the last answer my little sister did that :)

3. octoberchick1011

It's okay! No worries :) && Thank you SO much!