Is there an algebraic formula to find out the area of a hexagon?
1 Answer
Jun 3, 2018
Depending upon what properties are known:
# A = 3 a h # , or# A = (3sqrt(3))/2 \ a^2 #
Explanation:
Consider (as pictured:) a regular hexagon, with side length
# A_T = 1/2 xx "base" xx "height #
# \ \ \ \ \ = 1/2 a h #
Thus the area of the entire hexagon, is given by:
# A = 6 A_T #
# \ \ = 6/2 a h #
# \ \ = 3 a h #
If
# a^2 = h^2 + (a/2)^2 #
# \ \ \ = h^2 + a^2/4 #
# :. h^2 = (3a^2)/4 #
# h = (sqrt(3)a)/2 #
Thus we can write:
# A = (3) xx (a) xx ((sqrt(3)a)/2) #
# \ \ \ = (3sqrt(3))/2 \ a^2 #