a solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 ft and an area of…

Explanation:

Step1: Recall volume formula

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height.

Step2: Identify base - area and height

We are given that the base - area $B = 8$ ft². From the right - triangle formed with the height, we know that the horizontal distance from the center of the pentagonal base to a vertex of the base is related to the right - triangle with angle $\angle ACB=30^{\circ}$ and the side adjacent to the angle is $7\sqrt{3}$ ft. In the right - triangle $ABC$, $\tan\angle ACB=\frac{h}{7\sqrt{3}}$. Since $\angle ACB = 30^{\circ}$ and $\tan30^{\circ}=\frac{\sqrt{3}}{3}$, we have $h = 7$ ft.

Step3: Calculate volume

Substitute $B = 8$ ft² and $h = 7$ ft into the volume formula $V=\frac{1}{3}Bh$. So $V=\frac{1}{3}\times8\times7=\frac{56}{3}\approx19$ ft³.

Answer:

$19$ ft³