Chapter 12.2, Problem 2CYP

To determine

To calculate : To find the surface area of triangular prism.

Answer to Problem 2CYP

The required surface area of triangular prism is $635.64{\text{mm}}^2$

Explanation of Solution

Given information : The given triangular prism is,

  

Formula used : The surface area of triangular prism is,

  $\begin{array}{l}S=L+2B\\ =Ph+2B\end{array}$

Where, L is lateral area and B is base area.

Calculation : Let first find the lateral area:

The base of the prism is right angle triangle with the legs 8 ft and 6 ft long. Using Pythagoras theorem to find the length of the Pythagoras of the base,

  $\begin{array}{l}{c}^2={12}^2+{12}^2\\ =144+144\\ c=16.97\end{array}$

The required lateral area is,

  $\begin{array}{l}L=\left[16.97+12+12\right]\left[12\right]\\ =491.64{\text{mm}}^2\end{array}$

The required surface area is,

  $\begin{array}{l}S=Ph+2B\\ =491.64+2\left(\frac{1}{2}\cdot 12\cdot 12\right)\\ =635.64{\text{mm}}^2\end{array}$