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.
The side length = p / 6
A = (6) (1/2) (p/6)^2 sin (60°)
3/2 = 3 (p^2 / 36) sqrt (3) / 2
1 = sqrt (3) * p^2 / 36
36 / sqrt (3) = p^2
36/ 3^(1/2) = p^2 take the +sqrt of both sides
p = 6 / 3^(1/4)
Side length = [ 6/ 3^(1/4)] / 6 = 1/3^(1/4) ≈ .759
+1557 
