Question

a solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 ft and an area of 8 ft². angle acb measures 30°. what is the volume of the pyramid, to the nearest cubic foot? 5 ft³ 9 ft³ 14 ft³ 19 ft³

Explanation:

Step1: Find pyramid height

In right triangle $ABC$, $\tan(30^\circ)=\frac{\text{height}}{BC}$. Given $BC=7\sqrt{3}$ ft, so:
$\text{height}=BC\times\tan(30^\circ)=7\sqrt{3}\times\frac{1}{\sqrt{3}}=7$ ft

Step2: Calculate pyramid volume

Use volume formula $V=\frac{1}{3}\times\text{base area}\times\text{height}$. Base area $=8$ ft²:
$V=\frac{1}{3}\times8\times7=\frac{56}{3}\approx18.67$ ft³

Step3: Round to nearest cubic foot

$\approx19$ ft³

Answer:

19 ft³