Chapter SH, Problem 12.5.6EP

To determine

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

Answer to Problem 12.5.6EP

The lateral area and surface area are respectively ${\text{120in}}^2,132{\text{in}}^2$ .

Explanation of Solution

Given:

Dimensions of triangular prism are 3 in by 4 in by 5 in.

Height is 10 in.

Formula used:

Lateral area of the prism is $L=Ph$

Total surface area of the prism is $S=L+2B$

Calculation:

Lateral area of the prism is

  $L=Ph$

Here P is the base perimeter and h is the height.

Total surface area of the prism is

  $S=L+2B$

Here 2B is the area of two bases.

Perimeter of the base of a triangular prism is

  $\begin{array}{c}P=\text{sum of sides}\\ =3+4+5\\ =12\end{array}$

Area of the base is $\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)$

$\begin{array}{c}B=\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)\\ =\frac{1}{2}\left(3\right)\left(4\right)\\ =6\end{array}$

Height is h = 10 in.

Lateral area is

  $\begin{array}{c}L=Ph\\ =12\times 10\\ =120\end{array}$

Surface area is

  $\begin{array}{c}S=L+2B\\ =120+2\times 6\\ =132\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively ${\text{120in}}^2,132{\text{in}}^2$ .