Question

1. the dimensions of a rectangular prism is shown in the diagram. what is the total surface area of the prism?

Explanation:

Step1: Identify 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 \( SA = 2(lw + lh + wh) \). However, we need to check the units first. The length is given in yards (20 yd) and the other dimensions in inches (10 in, 8 in). This is a unit inconsistency. Wait, maybe it's a typo, and all should be in the same unit. Let's assume the 20 yd is a typo and should be 20 in (since the other dimensions are in inches). So \( l = 20 \) in, \( w = 8 \) in, \( h = 10 \) in.

Step2: Substitute the values into the formula

First, calculate each product:

• \( lw = 20 \times 8 = 160 \)
• \( lh = 20 \times 10 = 200 \)
• \( wh = 8 \times 10 = 80 \)

Step3: Sum these products and multiply by 2

Sum: \( 160 + 200 + 80 = 440 \)
Then, \( SA = 2 \times 440 = 880 \) square inches.

(Note: If the 20 yd is correct, we would need to convert yards to inches: 1 yd = 36 in, so 20 yd = 20×36 = 720 in. Then \( l = 720 \) in, \( w = 8 \) in, \( h = 10 \) in. Then \( lw = 720×8 = 5760 \), \( lh = 720×10 = 7200 \), \( wh = 8×10 = 80 \). Sum: 5760 + 7200 + 80 = 13040. Then \( SA = 2×13040 = 26080 \) square inches. But this seems too large, so the typo assumption is more likely. Given the diagram, probably 20 in. So we'll proceed with \( l = 20 \) in, \( w = 8 \) in, \( h = 10 \) in.)

Step1 (corrected with consistent units): Use the surface area formula

\( SA = 2(lw + lh + wh) \), where \( l = 20 \) in, \( w = 8 \) in, \( h = 10 \) in.

Step2: Calculate each term

\( lw = 20 \times 8 = 160 \)
\( lh = 20 \times 10 = 200 \)
\( wh = 8 \times 10 = 80 \)

Step3: Sum the terms and multiply by 2

Sum: \( 160 + 200 + 80 = 440 \)
\( SA = 2 \times 440 = 880 \)

Answer:

The total surface area of the prism (assuming the length is 20 inches) is 880 square inches. If the length is 20 yards, convert to inches (20×36 = 720 inches) and recalculate: \( SA = 2(720×8 + 720×10 + 8×10) = 2(5760 + 7200 + 80) = 2×13040 = 26080 \) square inches. But likely the 20 yd is a typo, so the answer is 880 square inches.