Geometry Apothem

Question

How do I find a side length of a regular polygon (triangle and hexagon) only given the area is 64.

Answer 1

Equilateral triangle:

Draw and label a diagram

The height is s√3/2. It is also the apothem!

This by 30-60-90 triangle

64 = (s/2)(s√3/2)(1/2)

128 = (s/2)(s√3/2)

512 = s²√3

295.60 ≈ s²

17.193 ≈ s

Answer 2

For a triangle the area formula is 1/2 (base times height).