the area of a regular hexagon is 500 what is the length of the radius?

Question

This is for Geometry class.

Answer 1

area of regular polygon = 1/2*apothem*perimeter

so 500 = 1/2 *apothem*perimeter

1000 = apothem * perimeter

perimeter of hexagon is 6 bases and apothem is sqrroot(3)/2*base

1000 = sqrroot(3)/2 *b*6b

1000 = 3sqroot(3) * b^2

 

so b^2 = 1000/3sqroot(3) or b^2 = 1000sqroot(3)/9

or b = sqroot [1000sqroot(3)] / 3

then b (radius) is approximately 13.87