Question

The dimensions of a rectangular prism are given in the net shown.
6 in. wide on the top
3 in. wide on the side
5 in tall
What is the total surface area of the rectangular prism in square inches?
Answers:
A. 90 in. squared
B. 145 in. squared
C. 126 in. squared
D. 96 in. squared

Answer 1

To calculate the total surface area of the rectangular prism, we need to find the surface area of each face of the prism and then sum them up.

Given:
- Width (W) = 6 inches (top)
- Depth (D) = 3 inches (side)
- Height (H) = 5 inches (tall)

The formula for the total surface area \( S \) of a rectangular prism is:

\[
S = 2(W \cdot H + H \cdot D + W \cdot D)
\]

Now, substituting the values into the equation:

1. \( W \cdot H = 6 \cdot 5 = 30 \)
2. \( H \cdot D = 5 \cdot 3 = 15 \)
3. \( W \cdot D = 6 \cdot 3 = 18 \)

Now add these areas:

\[
W \cdot H + H \cdot D + W \cdot D = 30 + 15 + 18 = 63
\]

Now multiply by 2 for the total surface area:

\[
S = 2 \cdot 63 = 126
\]

Thus, the total surface area of the rectangular prism is \( 126 \) square inches.

The correct answer is:

**C. 126 in. squared**