Chapter 12.3, Problem 42HP

To determine

Tofind:the lateral roof of area which is in the shape of a regular pentagonal pyramid.

Answer to Problem 42HP

The lateral area of regular pyramid is $172.5{\text{ ft}}^2$ and correct option is $C$ .

Explanation of Solution

Given:

  $\begin{array}{l}\left(A\right):34.5{\text{ ft}}^2.\\ \left(B\right):50{\text{ ft}}^2.\\ \left(C\right):172.5{\text{ ft}}^2.\\ \left(D\right):250{\text{ ft}}^2.\end{array}$:

Concept used:

The lateral area $L$ of a regular pyramid is $L=\frac{1}{2}pl$ .

Calculation:

The given figure is a regular pentagonal pyramid with $s=10\text{ ft and }l=6.9\text{ ft}$ .

The lateral area $L$ of a regular pyramid is $L=\frac{1}{2}Pl$ ,where $l$ is the slant height and $P$ is the perimeter of the base. Lateral area of a regular pyramid.

Formula of lateral area of regular pyramid shows that:

  $\begin{array}{l}L=\frac{1}{2}pl.\\ \Rightarrow \frac{1}{2}\left(5\left(10\right)\left(6.9\right)\right).\\ \Rightarrow \mathrm{172.5.}\end{array}$

Hence, the lateral area of regular pyramid is $172.5{\text{ ft}}^2$ and correct option is $C$ .