Surface Area
The figure shows a plane shape of a box
The box has sides 3x, x, and x
The surface area of the box is the sum of 6 rectangles: four of them have dimensions 3x by x. Two of them have dimensions x by x.
First, we compute the area of the rectangle of 3x by x:
[tex]A1=(3x)(x)=3x^2[/tex]Now, we compute the area of the rectangle (square really) of x by x:
[tex]A2=(x)(x)=x^2[/tex]As mentioned, there are 4 rectangles of area A1 and 2 squares of area A2, thus the total surface area is:
[tex]\begin{gathered} At=4\cdot(3x^2)+2\cdot x^2 \\ At=12x^2+2\cdot x^2=14x^2 \end{gathered}[/tex]Since x= 6 in, the surface area of the geometric shape is
[tex]\begin{gathered} At=14\cdot(6in)^2 \\ At=14\cdot36in^2 \\ At=504in^2 \end{gathered}[/tex]