Chapter 12.2, Problem 9PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 9PPS

L = $24f{t}^2$

S = $36f{t}^2$

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 right angled triangle , whose sides are 4 ft. and 3 ft.

By Pythagorean Theorem , the length c of hypotenuse is $c=\sqrt{a^2+b^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=5$ft.

Perimeter of the base of the prism = P = 4+3+5 = 12 ft.

Lateral area = Ph

Substitute P = 12 , h = 2 ;

So , Lateral area = L = $Ph=12\cdot 2f{t}^2=24ft{.}^2$

Area of the base = B = $\frac{1}{2}(base\text{ of triangle)(height of triangle)=}\frac{1}{2}(3)(4)=6ft{.}^2$

Surface area of prism = L + 2B = 24+2(6) = 24 +12 = $36ft{.}^2$

Hence ,

L = $24f{t}^2$

S = $36f{t}^2$