Question

Find the surface area of this rectangular prisms be sure to include the correct units in your answer

Answer 1

212 in²

Step-by-step explanation

The surface area of a prism is the sum of the areas of each face of the prism. For a rectangular prism, all faces are rectangles and they are in pairs - meaning that there are 3 different sizes of rectangles and there are 2 faces of each size.

First let's find the area of the top and the base. Both have the same shape and, in this case, they are formed by the largest rectangle: 9in wide by 8 in long:

`A_{\text{base}}=A_{\text{top}}=9in*8in=72in^2`

Then we have the left and right faces, which are 2in long by 8 inches wide:

`A_{\text{left}}=A_{\text{right}}=2in*8in=16in^2`

And finally the front and the back faces, 9 in wide by 2 in long:

`A_{\text{back}}=A_{\text{front}}=9in*2in=18in^2`

Now we just add twice each of these areas:

`SA=2A_{\text{base}}+2A_{\text{left}}+2A_{\text{back}}`
`\begin{gathered} SA=2\cdot72in^2+2\cdot16in^2+2\cdot18in^2 \\ SA=144in^2+32in^2+36in^2 \\ SA=212in^2 \end{gathered}`