Question

If X = 2 units, Y = 10 units, and Z = 7 units, then what is the surface area of the rectangular prism shown above?
A.
104 square units
B.
140 square units
C.
88 square units
D.
208 square units

Answer 1

To calculate the surface area of a rectangular prism, we use the formula:

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

where \( l \), \( w \), and \( h \) are the lengths of the sides of the rectangular prism. In this case, we can let:

- \( l = X = 2 \) units
- \( w = Y = 10 \) units
- \( h = Z = 7 \) units

Now, we substitute these values into the surface area formula:

\[
\text{Surface Area} = 2(2 \cdot 10 + 2 \cdot 7 + 10 \cdot 7)
\]

Calculating each term inside the parentheses:

1. \( 2 \cdot 10 = 20 \)
2. \( 2 \cdot 7 = 14 \)
3. \( 10 \cdot 7 = 70 \)

Now, add these results together:

\[
20 + 14 + 70 = 104
\]

Next, we multiply this sum by 2:

\[
\text{Surface Area} = 2 \cdot 104 = 208 \text{ square units}
\]

Therefore, the surface area of the rectangular prism is:

\[
\text{Surface Area} = 208 \text{ square units}
\]

The correct answer is \( \boxed{208} \) square units.