Question

the length,width, and height of a rectangular prism can be represented by the expressions (x+3), (x+7) and (x-1). Write an expression to represent the surface area of the prism.

Answer 1

The surface area = 2LW + 2LH + 2WH     where W = width, L = length and H = height 

So here we have 
Surface Area =  2(x+3)(x+7) + 2(x+3)(x-1) + 2((x+7)(x-1)

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

=  6x^2 + 36x + 22 

Answer 2

The expression that represents the surface area of the given prism is;

SA = 6x² + 36x + 22

Formula for surface area of a rectangular prism is given by;

SA = 2(LW + WH + LH)

Where;

W is width

H is height

L is length

Now, we are given;

Length; L = x + 3

Width; W = x + 7

Height; H = x - 1

Thus plugging in the relevant values into the surface area equation gives;

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

Solving the bracket gives;

SA = 2(x² + 10x + 21 + x² + 6x - 7 + x² + 2x -3)

SA = 2(3x² + 18x + 11)

SA = 6x² + 36x + 22

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