Chapter 12.3, Problem 2BCYP

To determine

To find:

The surface area of square pyramid.

Answer to Problem 2BCYP

The surface area of the pyramid is ${\text{360 m}}^2$ .

Explanation of Solution

Given information:

Square pyramid with a base of $10\text{ m}$ and a lateral height of $13\text{ m}$ .

Calculation:

The surface area $S$ of a regular pyramid is $S=L+B$ .

  $L$ is denoted as the lateral area.

  $L=\frac{1}{2}Pl$ , where $l$ is the slant height, $P$ is the perimeter of the base and $B$ is the area of the base.

Here, the base of $\text{10 m}$ and the slant height is $13\text{ m}$ .

  $\begin{array}{c}L=\frac{1}{2}Pl\\ =\frac{1}{2}\left(4\cdot 10\right)\left(13\right)\\ =2\cdot 10\cdot 13\\ =260\end{array}$

The surface area $S$ of a regular pyramid is $S=L+B$ .

  $\begin{array}{c}S=260+{\left(10\right)}^2\\ =260+100\\ =360\end{array}$

Hence, the surface area of the pyramid is ${\text{360 m}}^2$ .