the area of a regular hexagon is given as 384√3

Question

a. how long is each side of a hexagon
b. find the radius of a hexagon
c. find the apothem of a hexagon

Answer 1

Your hexagon consists of 6 equal equilateral triangles, of course the angle
would be 60°
If the side of the hexagon is x,
then the area of each triangle = (1/2)(x)(x)sin60° = √3 / 4 x^2
you have 6 of them, so the area of the hexagon = 6√3/4x^2
= (3/2)√3 x^2

then (3/2)√3 x^2 = 384√3
x^2 = 256
x = 16

I bet you can finish it from here