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 , 7in, 9.1 in
What is the total surface area of the box in square inches?
To find the total surface area of the rectangular prism, we need to find the area of each face and sum them up.
The rectangular prism has 6 faces: 2 rectangular faces on the top and bottom, and 4 rectangular faces on the sides.
The area of each rectangular face is found by multiplying its length and width.
For the top and bottom faces:
Area of the top face = Length * Width
= 10.5 in * 9.1 in
= 95.55 in² (rounded to two decimal places)
Since the top and bottom faces are identical, their total area is twice the area of one of the faces = 2 * 95.55 in² = 191.10 in² (rounded to two decimal places)
For the side faces:
Area of each side face = Length * Width
= 10.5 in * 7 in
= 73.5 in²
Since there are 4 side faces, their total area is 4 * 73.5 in² = 294 in²
The total surface area of the box is the sum of the areas of all its faces:
Total surface area = Area of top and bottom faces + Area of side faces
= 191.10 in² + 294 in²
= 485.10 in² (rounded to two decimal places)
Therefore, the total surface area of the box is 485.10 square inches.