Chapter 12.7, Problem 1CYU

To determine

To find: the lateral and surface area

Answer to Problem 1CYU

The surface area of the square pyramid is $533{\text{m}}^2$ andthe lateral area of the square pyramid is $364{\text{m}}^2$ .

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 13 m.

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

As side

Substitute side = 13 in the perimeter formula to find the perimeter of the square.

Thus,

  $\begin{array}{c}P=4\cdot 13\\ =52\end{array}$

The slant height of the square pyramid is 14 m

Substitute P = 52 and l = 14 in the lateral surface area to find the lateral surface area of the square pyramid.

  $\begin{array}{c}L=\frac{1}{2}Pl\\ =\frac{1}{\cancel{2}}\cdot 52\cdot \cancel{1}{\cancel{4}}^7\\ =52\cdot 7\\ =364\end{array}$

Therefore, the lateral area of the square pyramid is $364{\text{m}}^2$ .

Find the surface area of the square pyramid.

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

  $\begin{array}{c}B={\left(side\right)}^2\\ ={13}^2\\ =169\end{array}$

Substitute B = 169 and L = 364 in the surface area formula to find the surface area of the square pyramid.

  $\begin{array}{c}S=L+B\\ =364+169\\ =533\end{array}$

Conclusion:

Therefore, the surface area of the square pyramid is $533{\text{m}}^2$ andthe lateral area of the square pyramid is $364{\text{m}}^2$ .