+1911 A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.
+129850 If we inscribe the hexagon in a circle, the radius of the circle = the side length of the hexagon
The hexagon is composed of 6 equilateral triangles each having an area =
(1/2)r^2 sin (60°) = (1/2)r^2 * sqrt (3) / 2
So
A = 6 (1/2) r^2 * sqrt (3) / 2
3/2 = 3r^2 *sqrt (3) / 2
1 = r^2 sqrt (3)
1 / sqrt (3) = r^2
r = 1 / 3^(1/4) ≈ .76 = side of the hexagon
