Chapter 12.2, Problem 10PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 10PPS

L = $126m^2$

S = $151.8m^2$

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 hexagon , whose 4 sides measure 2m and 2 sides measure 3m.

Perimeter of the base of the hexagon = 4(2) + 2(3) = 14 m

Lateral area = Ph

Substitute P = 14 , h = 9 ;

So , Lateral area = L = $Ph=14\cdot 9m^2=126m^2$

The base is made up of a rectangle and two congruent triangles.

The area of the rectangle = $3\cdot 3=9m^2$

The height of the triangle of = $\sqrt{2^2-{\left(\frac{3}{2}\right)}^2}=\sqrt{\frac{7}{4}}\approx 1.3m$ [By Pythagorean Theorem , hypotenuse = 2 m , base = 1.5 m]

Area of the two triangles = $2\cdot \frac{1}{2}\cdot 3(1.3)=3.9m^2$ [ base = 3 m , height = 1.3 m]

Area of the base of the prism = B = $9+3.9=12.9m^2$

Surface area of prism = L + 2B = 126+2(12.9) = $126+25.8=151.8m^2$

Hence ,

L = $126m^2$

S = $151.8m^2$