Question

1. The length, width, and height of a rectangular prism can be represented by the expressions (r + 3),

(x + 7) and (x - 1). Write an expression to represent the surface area of the prism.​

Answer 1

6x² + 36x + 22

Explanation:

2 faces (x + 3) by (x + 7), area of both these faces 2(x+3)*(x + 7)

2 faces (x + 3) by (x - 1), area of both these faces 2(x+3)*(x - 1)

2 faces (x -1 ) by (x + 7), area of both these faces 2(x-1)*(x + 7)

Whole surface area is

2(x+3)*(x + 7) + 2(x+3)*(x - 1) + 2(x-1)*(x + 7) =

=2(x² + 3x +7x +21) + 2(x² +3x -x - 3) + 2(x² - x +7x -7)=

=2x² + 20x +42 + 2x² + 4x - 6 + 2x² + 12x -14 =

= 6x² + 36x + 22