Chapter 12.5, Problem 2CYU

To determine

To find: the lateral and surface area of prism.

Answer to Problem 2CYU

The surface area of the triangular prism is $480{\text{mm}}^2$ .

The lateral area of the triangular prism is $360{\text{mm}}^2$ .

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 given figure is a triangular prism.

The objective is to find the lateral and surface area of the triangular prism.

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.

The base of the prism is a triangle whose sides are 8 mm, 15 mm and 17 mm. Find the lateral area of the triangular prism as follows:

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.

  $\begin{array}{c}P=l_1+l_2+l_3\\ =8+15+17\\ =40\end{array}$

The lateral area of the triangular prism is,

Substitute P = 40 and h = 9 in $L=P\cdot h$

Thus,

  $\begin{array}{c}L=P\cdot h\\ =40\cdot 9\\ =360\end{array}$

Therefore, the lateral area of the triangular prism is $360{\text{mm}}^2$ .

Find the surface area of the triangular prism as follows:

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

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

  $\begin{array}{c}B=\frac{1}{2}\cdot b\cdot a\\ =\frac{1}{\cancel{2}}\cdot 15\cdot {\cancel{8}}^4\\ =15\cdot 4\\ =60\end{array}$

Substitute B = 60 and L = 360 in S = L + 2B

  $\begin{array}{c}S=L+2B\\ =360+2\cdot 60\\ =360+120\\ =480\end{array}$

Conclusion:

Therefore, the surface area of the triangular prism is $480{\text{mm}}^2$ and the lateral area of the triangular prism is $360{\text{mm}}^2$ .