Chapter 12, Problem 3PT

To determine

To calculate : The surface area of the tent.

Answer to Problem 3PT

The surface area of the tent would be $943.6f{t}^2$

Explanation of Solution

Given information : A right triangular prism is given base side is 14 ft, the base height 8 ft, and the length of the tent is 18 ft.

  

Formula used : The surface area of the tent would be the base area plus the lateral area of the tent. And the lateral surface area of the triangular prism is $ph$ . Also, the base area of both bases would be $ab$ . And the slant side is $l=\sqrt{a^2+b^2}$ . Where $p$ is the perimeter of the base and $h$ is the length of the prism and $a$ , $b$ are the base side and base height. And the perimeter will be the sum of the base sides.

Calculation : Calculate the slant height.

  $l=\sqrt{a^2+b^2}$

  $\begin{array}{l}l=\sqrt{{14}^2+8^2}\\ l=\sqrt{196+64}\\ l=16.1ft\end{array}$

Now, calculate the perimeter of the base

  $\begin{array}{l}p=a+l+l\\ p=14+16.1+16.1\\ p=46.2ft\end{array}$

Calculating the lateral surface area now.

  $\begin{array}{l}L=ph\\ L=46.2\times 18\\ L=831.6f{t}^2\end{array}$

Now, calculate the base area of both bases.

  $\begin{array}{l}=ab\\ =14\times 8\\ =112f{t}^2\end{array}$

The surface area of the tent would be the base area plus the lateral area of the tent.

  $\begin{array}{l}=112f{t}^2+831.6f{t}^2\\ =943.6f{t}^2\end{array}$