Question

heron deconstructs a box to put in the recycling bin. when the is flattened, it has the shape shown below. what is the total surface area of the box? a. 110 square inches b. 158 square inches c. 79 square inches d. 128 square inches

Explanation:

Step1: Identify the dimensions of the box

The box is a rectangular prism. From the net, we can see that the length \( l = 8 \) in, the width \( w = 5 \) in, and the height \( h = 3 \) in.

Step2: Recall the formula for the surface area of a rectangular prism

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \).

Step3: Substitute the values into the formula

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 8 \times 5 = 40 \)
• \( lh = 8 \times 3 = 24 \)
• \( wh = 5 \times 3 = 15 \)

Then, substitute these into the formula:
\( SA = 2(40 + 24 + 15) \)
\( SA = 2(79) \)
\( SA = 158 \) square inches.

Answer:

B. 158 square inches