Question

What is the total surface area of a rectangular prism with the dimensions of 2 centimeters, 5 centimeters, and 6 centimeters?

Answer 1

To find the total 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.

For the given dimensions:
- Length \( l = 2 \) cm
- Width \( w = 5 \) cm
- Height \( h = 6 \) cm

Using the formula, we first compute each product:

1. \( lw = 2 \times 5 = 10 \) cm²
2. \( lh = 2 \times 6 = 12 \) cm²
3. \( wh = 5 \times 6 = 30 \) cm²

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

\[
\text{Surface Area} = 2(10 + 12 + 30)
\]

Calculating the sum inside the parentheses:

\[
10 + 12 + 30 = 52
\]

Now, multiply by 2:

\[
\text{Surface Area} = 2 \times 52 = 104 \text{ cm}^2
\]

Thus, the total surface area of the rectangular prism is

\[
\boxed{104} \text{ cm}^2.
\]