Question

A solid oblique pyramid has a regular pentagonal base. The base has a edge length of 2.16 ft and and area of 8 ft^2. Angle ABC measures 30 degrees. What is the volume of the pyramid, to the nearest cubic foot?

Answer 1

Volume of the pyramid:

V = 1/3 · B · h

B = 8 ft²

tan 30° = height / 7√3

1/√3 = height / 7√3

height = 7 ft

V = 1/3 · 8 · 7 = 18.67 ft³ ≈ 19 ft³

Answer : D ) 19 ft³

Answer 2

The formula to compute the area for a solid oblique pyramid which has a regular pentagonal base is V=1/3*h*B where "h" represent the height and "B" for the area of the base.
In the given problem area is given which is equal to 8ft² and height is 2.16. Then we can solve for the volume such as shown below:
V=1/3*2.16*8
V=5.76 ft³