Chapter 12, Problem 5CT

To determine

To find: The total area of right triangular prism.

Answer to Problem 5CT

The total area right triangular prism is $660$ square units.

Explanation of Solution

Given information:The base edges of right triangular prism are 5, 12, 13, and the height is 20.

Calculation:

The formula to calculate Base Area( $BA$ ) of right triangular prism is:

  $BA=\frac{1}{2}\times \text{base of triangle}\times \text{height}$

Substitute 5 for base and 12 for $h$ in above formula.

  $\begin{array}{c}BA=\frac{1}{2}\times 5\times 12\\ =5\times 6\\ =30\end{array}$

The perimeter $p$ of triangle is:

  $\begin{array}{c}p=5+12+13\\ =30\end{array}$

Total Areaof right triangular prism can be calculated as:

  $\begin{array}{c}\text{Total}\text{area}=ph+2BA\\ =30\times 20+2\times 30\\ =600+60\\ =660\end{array}$

Therefore, the total area of right triangular prism is $660$ square units.