Chapter 12.7, Problem 5PPS

To determine

To find: the lateral and surface area

Answer to Problem 5PPS

The surface area of the square pyramid is $340{\text{in}}^2$ and the lateral area of the square pyramid is $240{\text{in}}^2$

Explanation of Solution

Given:

  

Formula used:

The lateral area L of a square pyramid is $L=\frac{1}{2}Pl$

The surface area S of a square pyramid is S = L + B

Calculation:

The given figure is a square pyramid.

The objective is to find the lateral and surface area of the square pyramid.

Find the lateral area of the square pyramid.

The side of the square is 10 in.

The perimeter P of the square is P = 4(side)

Substitute side= 10 in the perimeter formula to find the perimeter of the square.

Thus,

  $\begin{array}{c}P=4\cdot 10\\ =40\end{array}$

The slant height of the square pyramid is 12 in.

Substitute P = 40 and l = 12 in $L=\frac{1}{2}Pl$

  $\begin{array}{c}L=\frac{1}{2}Pl\\ =\frac{1}{\cancel{2}}\cdot 40\cdot \cancel{1}{\cancel{2}}^6\\ =40\cdot 6\\ =240\end{array}$

Therefore, the lateral area of the square pyramid is $240{\text{in}}^2$

Find the surface area of the square pyramid as shown below:

The area B of the square pyramid is, $B={\left(side\right)}^2$

  $\begin{array}{c}B={\left(side\right)}^2\\ ={10}^2\\ =100\end{array}$

Substitute B= 100 and L= 240 in the surface area formula to find the surface area of the square pyramid.

  $\begin{array}{c}S=L+B\\ =240+100\\ =340\end{array}$

Conclusion:

Therefore, the surface area of the square pyramid is $340{\text{in}}^2$ and the lateral area of the square pyramid is $240{\text{in}}^2$