Chapter 12.5, Problem 13PPS

To determine

The surface area of the each prism:

  

Answer to Problem 13PPS

The surface area of the prismis $656m^2$

Explanation of Solution

Given:

  

  $\begin{array}{l}L=14m\\ h_1=10m\\ l=8m\\ w=s_3=8m\\ s_2=10m\\ H=8m\end{array}$

Concept Used:

The surface area of the rectangular prism is given by the following expression:

  $SA=2\left(wl+hl+hw\right)$

Where,

Length of rectangular prism: $l$

Widthof rectangular prism: $w$

Height of rectangular prism: $h$

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:

In the given figure there isone triangular prism and one rectangular prism so number each volume as:

  

  $\begin{array}{l}{s}_1=h_2=14-10=4m\\ s_2=10m\\ s_3=8m\end{array}$

The surface area of the triangular prism 1:

  $\begin{array}{l}S{A}_1=bh+\left(s_1+s_2+s_3\right)H\\ S{A}_1=b{h}_2+\left(s_1+s_2+s_3\right)H\\ S{A}_1=\left(8\times 4\right)+\left(4+10+8\right)8\\ S{A}_1=32+176\\ S{A}_1=208m^2\end{array}$

The surface area of the rectangular prism2:

  $\begin{array}{l}S{A}_2=2\left(wl+hl+hw\right)\\ S{A}_2=2\left[\left(8\times 8\right)+\left(10\times 8\right)+\left(10\times 8\right)\right]\\ S{A}_2=448m^2\end{array}$

Total surface area of prism:

  $\begin{array}{l}SA=S{A}_1+S{A}_2\\ SA=208+448\\ SA=656m^2\end{array}$

Conclusion:

Hence, the surface areaof the prism is $656m^2$