Question

find the surface area of this rectangular prism. be sure to include the correct unit in your answer.

Explanation:

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

The formula for the surface area \( SA \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \).
From the diagram, we can identify that \( l = 8 \) in, \( w = 5 \) in, and \( h = 9 \) in.

Step2: Substitute the values into the formula

First, calculate each product:

• \( lw = 8\times5 = 40 \)
• \( lh = 8\times9 = 72 \)
• \( wh = 5\times9 = 45 \)

Then, add these products together: \( 40 + 72 + 45 = 157 \)

Next, multiply the sum by 2: \( SA = 2\times157 = 314 \)

Answer:

The surface area of the rectangular prism is \( 314 \) square inches.