Chapter 12, Problem 5PT

To determine

To calculate : The lateral area and the surface area of the square pyramid.

Answer to Problem 5PT

The lateral area of the prism would be $40c{m}^2$. And the total surface area would be $56c{m}^2$

Explanation of Solution

Given information : A square pyramid with a base side 4 cm and the slant height is 5 cm.

Formula used : The lateral surface area of a square pyramid is $L=\frac{1}{2}(pl)$ . And the total surface area would be $S=a^2+\frac{1}{2}(pl)$ . Where $p$ is the perimeter of the base and $l$ is the slant height of the pyramid and $a$ is the base side. And the perimeter will be the sum of the base sides.

Calculation : Calculate the perimeter of the base

  $\begin{array}{l}p=a+a+a+a=4a\\ p=4\times 4\\ p=16cm\end{array}$

Calculating the lateral surface area now.

  $\begin{array}{l}L=\frac{1}{2}(pl)\\ L=\frac{1}{2}(16\times 5)\\ L=40c{m}^2\end{array}$

Now, calculate the total surface area.

  $\begin{array}{l}S=a^2+\frac{1}{2}(pl)\\ S=4^2+\frac{1}{2}(16\times 5)\\ S=16+40\\ S=56c{m}^2\end{array}$