Chapter SH, Problem 12.7.5EP

To determine

To find: the lateral area and surface area of Square pyramid

Answer to Problem 12.7.5EP

The lateral area and surface area are $10.8m{m}^2,14.04m{m}^2$ .

Explanation of Solution

Given:

Length of base side is $1.8mm$ .

Slant height is $3.0mm$ .

Formula used:

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.

Here base is a square.

Perimeter of the base is

  $\begin{array}{l}P=4(side)\\ =4\times 1.8\\ P=7.2\end{array}$

Slant height is $I=3$ .

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

  $\begin{array}{l}$ B={(side)}^2$={1.8}^2\\ =3.24\end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 7.2\times 3\\ =10.8\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =10.8+3.24\\ =14.04\end{array}$

Hence, the lateral area and surface area are $10.8m{m}^2,14.04m{m}^2$ .

Conclusion:

Hence, the lateral area and surface area are $10.8m{m}^2,14.04m{m}^2$ .