Shavon has a gift box shaped like a rectangular prism the box is 12in long 8in wide and 3in high what is the surface area of the gift box

Answer 1

To find the surface area of a rectangular prism, you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where:

• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

Given:

• Length \( l = 12 \) inches
• Width \( w = 8 \) inches
• Height \( h = 3 \) inches

Now, we can calculate the surface area step by step.

1. Calculate the area of each pair of opposite faces:

   • Area of the length and width faces: \( lw = 12 \times 8 = 96 \) square inches
   • Area of the length and height faces: \( lh = 12 \times 3 = 36 \) square inches
   • Area of the width and height faces: \( wh = 8 \times 3 = 24 \) square inches

2. Now, sum these areas: \[ lw + lh + wh = 96 + 36 + 24 = 156 \]

3. Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 156 = 312 \text{ square inches} \]

Therefore, the surface area of the gift box is 312 square inches.