Question

determine the total surface area of the prism step 1: label all dimensions. step 2: calculate the area of each pair of faces. step 3: add the area of each face. a. $31\\,\mathrm{cm}^2$ b. $50\\,\mathrm{cm}^2$ c. $42\\,\mathrm{cm}^2$ d. $62\\,\mathrm{cm}^2$

Explanation:

Step 1: Identify the dimensions of the rectangular prism

From the net, the length \( l = 5 \) in, width \( w = 3 \) in, and height \( h = 2 \) in.

Step 2: Use the formula for the surface area of a rectangular prism

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

Substitute \( l = 5 \), \( w = 3 \), and \( h = 2 \) into the formula:
\[

$$\begin{align*} SA &= 2((5\times3) + (5\times2) + (3\times2)) \\ &= 2(15 + 10 + 6) \\ &= 2(31) \\ &= 62 \end{align*}$$

\]

Answer:

D. \( 62 \, \text{cm}^2 \) (Note: The units should be consistent, and if the original dimensions are in inches, the area should be in square inches, but following the given options, the answer is D.)