Chapter 12.3, Problem 39HP

To determine

To explain:

A pyramid that has a total surface area of $100$ square units.

Answer to Problem 39HP

A square pyramid with a base edge of $5$ units and a alant height of $7.5$ units has area $100$ square units.

Explanation of Solution

Given information:

A pyramid that has a total surface area of $100$ square units.

The surface area of the pyramid is given as:

  $S=\frac{1}{2}Pl+s^2$

By using hit and trail method assume a square pyramid with a base edge of $5$ units and a alant height of $7.5$ units.

  $\begin{array}{c}S=\frac{1}{2}\left(4\cdot 5\right)\left(7.5\right)+5^2\\ =10\left(7.5\right)+25\\ =75+25\\ =100\end{array}$

Hence, a square pyramid with a base edge of $5$ units and a alant height of $7.5$ units has area $100$ square units.