Question

PLEASE HELP ME I DONT UNDERSTAND

Answer 1

Lets get started :)

The surface area formula of a rectangular prism is:
S.A = 2 ( (width x height ) + ( length x width ) + ( length x height ) )

Given:
Height = x + 4
Width = x
Length = x + 2

S.A = 2 ( ( x )( x + 4 ) + ( x + 2 )( x ) + ( x + 2 )( x + 4 ) )
= 2 ( ( x² + 4x ) + ( x² + 2x ) + ( x² + 6x + 8 ) )
Combine like - terms together
= 2 ( 3x² + 12x + 8 )
= 6x² + 24x + 16

Your answer will be your first option

Answer 2

There are 6 faces in this prism. Each pair of opposite faces is two congruent faces.
The front and back faces have dimensions x by x + 4.
The right and left faces have dimensions x + 2 by x + 4.
The top and bottom faces have dimensions x by x + 2.

Let's find the area of each different face.

Front & back:
A = LW = x(x + 4) = x^2 + 4x

Right and left:
A = LW = (x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8

Top & bottom:
A = LW = x(x + 2) = x^2 + 2x

Now we add the three areas:
x^2 + 4x + x^2 + 6x + 8 + x^2 + 2x =

=3x^2 + 12x + 8

The polynomial above is the sum of the areas of three different faces.
Each of the three different faces has a congruent opposite face with the same area, so we double this area to find the total surface area of all 6 faces.

2(3x^2 + 12x + 8) = 6x^2 + 24x + 16

The answer is option A.