Blanca is going to use a box that is a rectangular prism for a card box at her son's birthday party. She will wrap and decorate the box. The dimensions of the box are shown in the diagram.
10.5 in., 9.1 in., 7 in.
What is the total surface area of the box in square inches?
To find the total surface area of the box, we need to calculate the area of each face and then sum them up.
The box has six faces.
- The top and bottom faces have the same dimensions as the length and width of the box, so they each have an area of 10.5 inches * 9.1 inches = 95.55 square inches.
- The front and back faces have the same dimensions as the height and width of the box, so they each have an area of 9.1 inches * 7 inches = 63.7 square inches.
- The left and right faces have the same dimensions as the height and length of the box, so they each have an area of 10.5 inches * 7 inches = 73.5 square inches.
To find the total surface area, we sum up the areas of all six faces:
Total Surface Area = 2 * (top face + front face + left face)
= 2 * (95.55 square inches + 63.7 square inches + 73.5 square inches)
= 2 * (232.75 square inches)
= 465.5 square inches.
Therefore, the total surface area of the box is 465.5 square inches.