# 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 #