Question

the dimensions of a rectangular prism are given in the net shown. what is the total surface area of the rectangular prism in square inches? a. 71 in.² b. 58 in.² c. 142 in.² d. 105 in.²

Explanation:

Step1: Identify the dimensions

From the net, the dimensions of the rectangular prism are length \( l = 7 \) in, width \( w = 5 \) in, and height \( h = 3 \) in.

Step2: Recall the surface area formula

The formula for the total surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \).

Step3: Substitute the values

Substitute \( l = 7 \), \( w = 5 \), and \( h = 3 \) into the formula:
\[

$$\begin{align*} SA &= 2((7\times5) + (7\times3) + (5\times3)) \\ &= 2(35 + 21 + 15) \\ &= 2(71) \\ &= 142 \end{align*}$$

\]

Answer:

C. \( 142 \text{ in}^2 \)