Chapter 12.2, Problem 3CYU

To determine

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

Answer to Problem 3CYU

The required lateral area is $288{\text{ft}}^2$ surface area of triangular prism is $336{\text{ft}}^2$

Explanation of Solution

Given information : The given triangular prism is,

  

Formula used : The lateral area and surface area of triangular prism is,

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

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

Calculation :

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,

  $\begin{array}{l}{c}^2=8^2+6^2\\ =64+36\\ c=10\end{array}$

The required lateral area is,

  $\begin{array}{l}L=\left[10+8+6\right]\left[12\right]\\ =288{\text{ft}}^2\end{array}$

The required surface area is,

  $\begin{array}{l}S=Ph+2B\\ =288+2\left(\frac{1}{2}\cdot 6\cdot 8\right)\\ =288+48\\ =336{\text{ft}}^2\end{array}$