Question

Find the surface area of the rectangular prism.
4 yd, 1 yd, 2 yd

Answer 1

To find the surface area of a rectangular prism, you can use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

Given the dimensions of the rectangular prism:
- \( l = 4 \) yd,
- \( w = 1 \) yd,
- \( h = 2 \) yd.

Now, plug these values into the formula:

1. Calculate the area of each face:
- \( lw = 4 \times 1 = 4 \) yd²,
- \( lh = 4 \times 2 = 8 \) yd²,
- \( wh = 1 \times 2 = 2 \) yd².

2. Sum these areas:
\[
lw + lh + wh = 4 + 8 + 2 = 14 \text{ yd}^2
\]

3. Now, multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 14 = 28 \text{ yd}^2
\]

Thus, the surface area of the rectangular prism is \( \boxed{28} \) square yards.