Question 404286
Since the perimeter of the hexagon is 150 m, it follows that each side length is 25 m and the area of the hexagon is equal to six times the area of an equilateral triangle of length 25.


We could find the area of such an equilateral triangle by drawing an altitude to the base, etc. but it's a little ugly and uninteresting. A quick way to do it is to use {{{A = a*b*sin(theta)/2}}} where {{{theta}}} is between sides a and b. Thus,


{{{A = (25^2)(sin 60)/2 = 625sqrt(3)/4}}}


Multiplying by 6, we obtain {{{6A = 1875sqrt(3)/2}}}.