Chapter 12.5, Problem 7PPS

To determine

To find: the lateral and surface area of prism.

Answer to Problem 7PPS

The surface area of the triangular prism is $5.6{\text{m}}^2$ .

The lateral area of the triangular prism is $3.92{\text{m}}^2$ .

Explanation of Solution

Given:

  

Formula used:

The lateral area L of a triangular prism is, $L=P\cdot h$ .

The surface area S of a triangular prism is, S = L + 2B.

Calculation:

The lateral area L of a triangular prism is, $L=P\cdot h$ .

Here, P is the perimeter of the base of the triangle and h is the height the triangular prism.

The surface area S of a triangular prism is, S = L + 2B.

Here, L is the lateral area and B is the area of the triangular base.

Find the lateral area of the triangular prism as follows:

The base of the prism is a triangle whose sides are 0.7 m, 2.4 m and 2.5 m.

The perimeter P of the base of the prism is, $P=\left(l_1+l_2+l_3\right)$ .

Here, $l_1+l_2+l_3$ are sides of the triangle.

  $\begin{array}{c}P=l_1+l_2+l_3\\ =0.7+2.4+2.5\\ =5.6\end{array}$

Substitute P = 5.6 and h = 0.7 in $L=P\cdot h$ .

  $\begin{array}{c}L=P\cdot h\\ =\left(5.6\right)\left(0.7\right)\\ =3.92\end{array}$

Therefore, the lateral area of the triangular prism is $3.92{\text{m}}^2$ .

Find the surface area of the triangular prism as follows:

Find the area B of the base of the prism is, $B=\frac{1}{2}\cdot b\cdot a$ .

Here, b is the base and a is the height of the triangle.

  $\begin{array}{c}B=\frac{1}{2}\cdot b\cdot a\\ =\frac{1}{\cancel{2}}\cdot \left(\cancel{2}.{\cancel{4}}^{1.2}\right)\cdot \left(0.7\right)\\ =\left(1.2\right)\left(0.7\right)\\ =0.84\end{array}$

Substitute B = 0.84 and L = 3.92 in S = L + 2B

  $\begin{array}{c}S=L+2B\\ =3.92+2\cdot \left(0.84\right)\\ =3.92+1.68\\ =5.6\end{array}$

Conclusion:

Therefore, the surface area of the triangular prism is $5.6{\text{m}}^2$ and the lateral area of the triangular prism is $3.92{\text{m}}^2$ .