Chapter 12.2, Problem 13PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 13PPS

L = $11.2m^2$

S = $13.6m^2$

Explanation of Solution

Given:

The prism is :

  

Formula Used:

The Lateral area L of a right prism is

L = Ph , where h is the height of the prism and P is the perimeter of a base.

The Surface area S of a right prism is

S = L + 2B , where L is its Lateral area and B is the area of a base.

Calculation:

The base of the prism is a triangle , whose sides are 1.5 m , 1.7 m , 2.4 m

Perimeter of the base of the prism = P = 1.5+1.7+2.4 = 5.6 m

Lateral area = Ph

Substitute P = 5.6 , h = 2 ;

So , Lateral area = L = $Ph=5.6(2)m^2=11.2m^2$

The base of the prism is a triangle , whose base is 2.4 m and height is 1m

Area of the base of prism = B = $\frac{1}{2}(base\text{ of triangle)(height of triangle)=}\frac{1}{2}(2.4)(1)=1.2m^2$

Surface area of prism = L + 2B = 11.2+2(1.2) = 11.2 +2.4 = $13.6m^2$

Hence ,

L = $11.2m^2$

S = $13.6m^2$