Question

Find the surface area of the following rectangular prism. 2 ft 8 ft 1 ft surface area = Tft² l​

Answer 1

Answer:

$52\; {\rm ft^{2}}$.

Step-by-step explanation:

In a rectangular prism, there are three pairs of rectangular faces opposite of each other, for a total of six faces. The surface area of faces opposite to each other are the same. The surface area of the rectangular prism is the sum of the area of all these six faces.

In this question, the length of the sides of the rectangular prism are $2\; {\rm ft}$, $8\; {\rm ft}$, and $1\; {\rm ft}$. The six faces would consist of these three pairs:

• Two of $2\; {\rm ft} \times 8\; {\rm ft}$ rectangles,
• Two of $2\; {\rm ft} \times 1\; {\rm ft}$ rectangles, and
• Two of $8\; {\rm ft} \times 1\; {\rm ft}$ rectangles.

The surface area of this rectangular prism is the sum of the area of these three pairs of rectangles. Again, note that each pair consist of two rectangles of the same size.

$\begin{aligned} & 2 \times (2\; {\rm ft} \times 8\; {\rm ft}) + 2\times (2\; {\rm ft} \times 1\; {\rm ft}) + 2\times (8\; {\rm ft} \times 1\; {\rm ft}) \\ =\; & 2\times (2\; {\rm ft} \times 8\; {\rm ft} + 2\; {\rm ft} \times 1\; {\rm ft} + 8\; {\rm ft} \times 1\; {\rm ft}) \\ =\; & 2 \times (26\; {\rm ft^{2}}) \\ =\; & 52\; {\rm ft^{2}} \end{aligned}$.