Question

1. the dimensions of a rectangular prism is shown in the diagram.

what is the total surface area of the prism?

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism.

The formula for the total surface area \( SA \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \).

Step2: Identify the length, width, and height from the diagram.

From the diagram, we have:

• Length \( l = 8.5 \) in,
• Width \( w = 5 \) in,
• Height \( h = 6.5 \) in.

Step3: Calculate each term inside the formula.

First, calculate \( lw \):
\( lw = 8.5 \times 5 = 42.5 \)

Next, calculate \( lh \):
\( lh = 8.5 \times 6.5 = 55.25 \)

Then, calculate \( wh \):
\( wh = 5 \times 6.5 = 32.5 \)

Step4: Substitute these values into the formula.

\( SA = 2(42.5 + 55.25 + 32.5) \)

First, add the terms inside the parentheses:
\( 42.5 + 55.25 + 32.5 = 130.25 \)

Then, multiply by 2:
\( SA = 2 \times 130.25 = 260.5 \)

Answer:

The total surface area of the rectangular prism is \( 260.5 \) square inches.