Juanita covered the outside of a gift box shaped
like a rectangular prism with paper. The box is 3.2
feet long, 2.1 feet wide, and 2.7 feet high. Which
of the following is closest to the total surface area
of this box?
Besides that, his answer makes no sense.
Surface area = 2( (3.2)(2.1) + (3.2)(2.7) + (2.1)(2.7) )
= from your choices, pick the one that comes closest to this.
To find the total surface area of the box, we need to calculate the area of each of its six sides and then add them together.
The rectangular prism has three pairs of opposite sides: a pair of length and width, a pair of length and height, and a pair of width and height. The formula to calculate the surface area is:
Surface Area = 2(length × width + length × height + width × height)
Let's calculate it step by step:
1. Calculate the area of the length and width sides:
- Length × Width = 3.2 ft × 2.1 ft = 6.72 sq ft
2. Calculate the area of the length and height sides:
- Length × Height = 3.2 ft × 2.7 ft = 8.64 sq ft
3. Calculate the area of the width and height sides:
- Width × Height = 2.1 ft × 2.7 ft = 5.67 sq ft
4. Add up the areas of all three pairs of sides:
- 6.72 sq ft + 8.64 sq ft + 5.67 sq ft = 21.03 sq ft
Therefore, the total surface area of the gift box is approximately 21.03 square feet.
L = length = 18 inches
H = height = 9 inches