Question

shavon has a gift box shaped like a rectangular prism. the box is 12 inches long, 8 inches wide, and 3 inches high. what is the surface area of the gift box? 312 in.² 288 in.² 184 in.² 156 in.²

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 \( SA = 2(lw + lh + wh) \).

Step2: Identify the values of \( l \), \( w \), and \( h \).

Given that \( l = 12 \) inches, \( w = 8 \) inches, and \( h = 3 \) inches.

Step3: Calculate each term inside the parentheses.

First, calculate \( lw \): \( lw = 12 \times 8 = 96 \).
Next, calculate \( lh \): \( lh = 12 \times 3 = 36 \).
Then, calculate \( wh \): \( wh = 8 \times 3 = 24 \).

Step4: Sum the terms inside the parentheses.

\( lw + lh + wh = 96 + 36 + 24 = 156 \).

Step5: Multiply by 2 to get the surface area.

\( SA = 2 \times 156 = 312 \)? Wait, no, wait. Wait, 96 + 36 is 132, 132 +24 is 156. Then 2156 is 312? But wait, let's check again. Wait, 128=96, 123=36, 83=24. 96+36=132, 132+24=156. 2*156=312. But wait, the options have 312, 288, 184, 156. Wait, maybe I made a mistake? Wait, no, the formula is correct. Wait, let's recalculate:

Wait, \( SA = 2(lw + lh + wh) \)

\( l = 12 \), \( w = 8 \), \( h = 3 \)

\( lw = 12*8 = 96 \)

\( lh = 12*3 = 36 \)

\( wh = 8*3 = 24 \)

Sum: 96 + 36 + 24 = 156

Multiply by 2: 2*156 = 312. So the surface area is 312 square inches.

Answer:

312 in.² (the first option)