Height of the pentagon = 9 ft
Edge of base = 3 ft
[tex] area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )} [/tex]
s is the length of any side = 3
n is the number of sides = 5
tan is the tangent function calculated in degrees
[tex] \\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4 ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852 [/tex]
Volume of the pentagon = area of base (height )
Volume of the pentagon = 15.4852 (9)
Volume of the pentagon = 139.366
Volume of the pentagon = 139.37 cu.ft
