Question

15 in 13.76 in 20 in volume = _

Explanation:

Step1: Find the base - area

The base is a regular pentagon. The formula for the area of a regular pentagon with side length $s$ and apothem $a$ is $A=\frac{1}{2}\times perimeter\times apothem$. The side - length of the pentagon $s = 20$ in, and the apothem $a=13.76$ in. The perimeter $P$ of a regular pentagon with side - length $s$ is $P = 5s$. So, $P=5\times20 = 100$ in. Then the base - area $A=\frac{1}{2}\times100\times13.76=688$ in².

Step2: Calculate the volume of the pyramid

The formula for the volume of a pyramid is $V=\frac{1}{3}Ah$, where $A$ is the base - area and $h$ is the height. Here, $A = 688$ in² and $h = 15$ in. So, $V=\frac{1}{3}\times688\times15$.
$V = 688\times5=3440$ in³.

Answer:

$3440$ in³