Chapter 12.1, Problem 8PSB

To determine

To calculate: The total area of the prism.

Answer to Problem 8PSB

The total area of the prism is $226$ .

Explanation of Solution

Given information:

A prism with rectangles of dimensions 2 by 7, 4 by 7 and 5 by 7.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle

Calculation:

  

Area of top and bottom rectangles $=2\left(4\times 2\right)+2\left(7\times 2\right)$

Area of top and bottom rectangles $=16+28$

Area of top and bottom rectangles $=44$

Area of front rectangles $=\left(4\times 7\right)+\left(5\times 7\right)+2\left(2\times 7\right)$

Area of front rectangles $=28+35+28$

Area of front rectangles $=91$

Area of back rectangles $=\left(7\times 6\right)+\left(7\times 7\right)$

Area of back rectangles $=42+49$

Area of back rectangles $=91$

Total area = Area of top and bottom rectangles + Area of front rectangles + Area of back rectangles

Total area $=44+91+91$

Total area $=226$