Chapter 12.2, Problem 16PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 16PPS

L = $216i{n}^2$

S = $324i{n}^2$

Explanation of Solution

Given:

The triangular prism : h = 6 inches, right triangle base with legs 9 inches and 12 inches.

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 legs are 9 inches and 12 inches

By Pythagorean Theorem , the length c of hypotenuse is $c=\sqrt{a^2+b^2}=\sqrt{9^2+{12}^2}=\sqrt{81+144}=15$inches

Perimeter of the base of the prism = P = 9 + 12 + 15 = 36 inches

Lateral area = Ph

Substitute P = 36 , h = 6 ;

So , Lateral area = L = $Ph=36(6)i{n}^2=216i{n}^2$

The base of the prism is a triangle , whose base is 9 inches and height is 12 inches

Area of the base of prism = B = $\frac{1}{2}(base\text{ of triangle)(height of triangle)=}\frac{1}{2}(9)(12)=54i{n}^2$

Surface area of prism = L + 2B = 216+2(54) = 216 + 108 = $324i{n}^2$

Hence ,

L = $216i{n}^2$

S = $324i{n}^2$