Chapter SH, Problem 12.7.3EP

To determine

To find: the lateral area and surface area

Answer to Problem 12.7.3EP

The lateral area and surface area are $72f{t}^2,88f{t}^2$ .

Explanation of Solution

Given:

Lateral area of the pyramid is $L=\frac{1}{2}PI$

Total surface area of the prism is $S=L+B$

Lateral area of the pyramid is

  $L=\frac{1}{2}PI$

Here $P$ is the base perimeter and $I$ is the slant height.

Total surface area of the prism is

  $S=L+B$

Here $B$ is the area of base.

Perimeter of the base is

  $\begin{array}{l}P=4\left(side\right)\\ =4\times 4\\ =16\\ P=16\end{array}$

Slant height is $I=9ft.$

Area of the base is ${\left(side\right)}^2$ .

  $\begin{array}{l}B={\left(side\right)}^2\\ =4^2\\ =16\end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 16\times 9\\ =72\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =72+16\\ =88\end{array}$

Hence, the lateral area and surface area are $72f{t}^2,88f{t}^2$ .

Conclusion:

Hence, the lateral area and surface area are $72f{t}^2,88f{t}^2$ .