Chapter 12.5, Problem 25STP

To determine

The surface area of the each prism and choose the correct option:

  

F. $1065c{m}^2$

G. $945c{m}^2$

H. $777c{m}^2$

J. $864c{m}^2$

Answer to Problem 25STP

Correct option is J. The surface area of the triangular prismis $864c{m}^2$

Explanation of Solution

Given:

  

  $\begin{array}{l}{s}_1=h=9cm\\ s_2=15cm\\ s_3=b=12cm\\ H=21cm\end{array}$

Concept Used:

The volume of the triangular prism is given by the following expression:

  $SA=bh+\left(s_1+s_2+s_3\right)H$

Where,

Length of each side of triangle: $\left(s_1,s_2,s_3\right)$

Base of triangular prism: $b$

Height of triangle: $h$

Height of triangular prism: $H$

Calculation:

The surface area of the triangular prism is given as:

  $\begin{array}{l}SA=bh+\left(s_1+s_2+s_3\right)H\\ SA=\left(12\times 9\right)+\left(9+15+12\right)21\\ SA=108+756\\ SA=864c{m}^2\end{array}$

Conclusion:

Hence, the surface areaof the prism is $864c{m}^2$