Question

If X = 7 units, Y = 4 units, and Z = 6 units, then what is the surface area of the rectangular prism shown above?
A.
94 square units
B.
204 square units
C.
188 square units
D.
168 square units

Answer 1

To calculate 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, and \( h \) is the height of the prism.

In this case, we have:
- \( l = X = 7 \) units
- \( w = Y = 4 \) units
- \( h = Z = 6 \) units

Now, we can substitute these values into the formula:

1. Calculate the area of each face:
- \( lw = 7 \times 4 = 28 \) square units
- \( lh = 7 \times 6 = 42 \) square units
- \( wh = 4 \times 6 = 24 \) square units

2. Add these values:
\[
lw + lh + wh = 28 + 42 + 24 = 94 \text{ square units}
\]

3. Now multiply by 2 to find the total surface area:
\[
\text{Surface Area} = 2 \times 94 = 188 \text{ square units}
\]

So, the surface area of the rectangular prism is:

**C. 188 square units**