The given figure is a pentagonal prism. Each side of the prism is 7ft. Since is has 5 equal sides, then te perimeter is
Perimeter = 5 * 7 = 35
The next step is to find the apotherm of the face of the prism. The apotherm, a is the shortest distance from the center point on the face of the prism to any side and it is perpendicular to that side. The formula for determining apotherm is expressed as
a = s/2tan(180/n)
where
s is the length of each face
n is the number of sides
Thus,
a = 7/2tan(180/5) = 7/2tan36
a = 4.82
We already know the area of each face which is
A = 84.3
Thus, we would calculate the volume by applying the formula,
Volume = 1/2(5s x a)h
h = 4
Volume = 1/2(5 x 7 x 4.82)4
Volume = 337.4 square feet