A regular hexagon has perimeter p and area A. Compute (p^2)/A

A regular hexagon is comprised of 6 equilateral triangles. Each side is s = p/6

Area of 1 triangle:  A1 = (1/2)*s*sqrt(s^2 - (s/2)^2) → (1/2)*s^2*sqrt(3/4) → (1/72)*p^2*sqrt(3/4) 

Area of hexagon;  A = 6A1 → (6/72)*p^2*sqrt(3/4) → (1/12)*p^2*sqrt(3/4) → (1/24)*p^2*sqrt(3)

Hence p^2/A = 24/sqrt(3) → 8sqrt(3)

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Let  P/6 be the side length

Area  =  6 *(1/2)(P/6)^2*sin(60)  = 3(P^2/36)√3/ 2   = [ 3√3/72 [ P^2  = [ √3/24 ]P^2

So

P^2 /A  =   P^2 /  [ √3/24 * P^2]  =   1 / [√3/24]  =    24 / √3   =    [ √3 * 24] / [ √3 *√3] =

√3 * 24  / 3  =   8√3