Question

If x = 6 in, what is the surface area of the geometric shape formed by this net?

Answer 1

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:

`A1=(3x)(x)=3x^2`

Now, we compute the area of the rectangle (square really) of x by x:

`A2=(x)(x)=x^2`

As mentioned, there are 4 rectangles of area A1 and 2 squares of area A2, thus the total surface area is:

`\begin{gathered} At=4\cdot(3x^2)+2\cdot x^2 \\ At=12x^2+2\cdot x^2=14x^2 \end{gathered}`

Since x= 6 in, the surface area of the geometric shape is

`\begin{gathered} At=14\cdot(6in)^2 \\ At=14\cdot36in^2 \\ At=504in^2 \end{gathered}`