Question

Find the surface area of the rectangular prism. Express your answer as a polynomial instandard form.

Answer 1

Given:

Length of the prism, L = x + 2

Width of prism, W = x + 4

Height of prism, H = x

To find the surface area, use the formula already given:

Surface Area = 2LW + 2LH + 2WH

Input the values into the formula:

Surface Area = 2(x+2)(x+4) + 2(x+2)(x) + 2(x+4)(x)

Expand the parentheses:

`2(x^2+6x+8)\text{ + 2(x}^2+2x)+2(x^2+4x)`

Use distributive property to multiply:

`2x^2+12x+16+2x^2+4x+2x^2+8x`

Collect like terms and evaluate:

`\begin{gathered} 2x^2+2x^2+2x^2+12x+4x+8x+16 \\ \\ =6x^2+24x+16 \end{gathered}`

Therefore, the surface area of the rectangular prism as a polynomial in standard form is:

`6x^2+24x+16`

ANSWER:

`6x^2+24x+16`