Question

Find the surface area of the rectangular prism.
7 in, 4 in, 6 in

Answer 1

To find the surface area \( S \) of a rectangular prism, you can use the formula:

\[
S = 2(lw + lh + wh)
\]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

Given the dimensions:
- Length (\( l \)) = 7 inches
- Width (\( w \)) = 4 inches
- Height (\( h \)) = 6 inches

Now, substitute the values into the formula:

1. Find the area of each pair of faces:
- \( lw = 7 \times 4 = 28 \)
- \( lh = 7 \times 6 = 42 \)
- \( wh = 4 \times 6 = 24 \)

2. Now, sum these areas:
\[
lw + lh + wh = 28 + 42 + 24 = 94
\]

3. Finally, calculate the total surface area:
\[
S = 2 \times 94 = 188 \text{ square inches}
\]

Therefore, the surface area of the rectangular prism is \( \boxed{188} \) square inches.