Question

How do I figure out the total surface area of the right prism?

Answer 1

The total surface area is the sum of the areas of all the faces that enclose the given prism. From the given information, the area of the two bases (denoted in dark blue) is equal to 16 square inches. This is because the base of the prism is a square with sides equal to 4 inches:

Then, we need to find the area of the four rectangular faces. Since the four faces have the same measure:

the lateral area is equal to four times the area of one rectangle, that is,

`\begin{gathered} LA=4*40in^2 \\ LA=160in^2 \end{gathered}`

Therefore, the total surface area (SA) is given by

`\begin{gathered} SA=2B+LA \\ SA=32+160 \\ SA=192in^2 \end{gathered}`

Therefore, the answer is 192 square inches.