Chapter 12.7, Problem 10PPS

To determine

To find: the lateral area of the square pyramid.

Answer to Problem 10PPS

The lateral area of the square pyramid is $42050{\text{ft}}^2$

Explanation of Solution

Given:

Slant height is 856 ft

Length of the side of the base is 145 ft.

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

Formula used:

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

Calculation:

The side of the square is 145 ft

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

Substitute side = 145 in the perimeter formula to find the perimeter of the square.

Thus,

  $\begin{array}{c}P=4\cdot 145\\ =580\end{array}$

The slant height of the square pyramid is 856 ft.

Substitute P = 580 and l = 856 in the lateral surface area to find the lateral surface area of the square pyramid.

  $\begin{array}{c}L=\frac{1}{2}Pl\\ =\frac{1}{\cancel{2}}\cdot \cancel{5}\cancel{8}{\cancel{0}}^{290}\cdot 145\\ =290\cdot 145\\ =42050\end{array}$

Conclusion:

Therefore, the lateral area of the square pyramid is $42050{\text{ft}}^2$