Question

I need help finding the area of a regular hexagon with an apothem of 6cm. No side length is given

Answer 1

The apothem is the perpendicular distance to the base, and you know that
all angles are 60°
You should the ratio of sides of the standard 30-60-90 triangle, you can see
such a triangle.
by simple ratios the base of such a triangle with height of 6 cm is 2√3
so each side of the hexagon is 4√3

area of one of the six triangles = (1/2)(4√3)(6) cm^2
= 12√3 cm^2
and since we have 6 of those .......

You could also find the side of the hexagon this way:
let each side be 2x,
then tan60° = 6/x
x = 6/tan60 = 6/√3
= 6/√3 * √3/√3
= 2√3
so each side is 2x = 4√3, just as before

Answer 2

tysm