a)
The hexagon is represented by simpler polygons because it's a six sided polygon or 6-gon. So the the total of the internal angles of any hexagon is 720°
triangle on left:
h = 11 - 7 = 4 ft
b = 24 - 14 = 10 ft
so hypo = √(4^2 + 10^2) = √(16 + 100) = √116 = 2√29 ft
triangle on the right:
b = 24 - 20 = 4 ft
h = 11 - 6 = 5 ft
so hypo = √(4^2 + 5^2) = √(16 + 25) = √41 ft
so dimensions of each of these simpler polygons:
√41 ft , 2√29 ft and given 7 ft, 20 ft, 6 ft , 14 ft
b)
area of rectangle = 24 x 11 = 264 ft^2
area of triangle on left = 1/2bh = 1/2(4)(10) = 20 ft^2
area of triangle on right = 1/2bh = 1/2(4)(5) = 10 ft^2
area of complex polygons
264 - 20 - 10 = 234 ft^2
answer: 234 ft^2
