Greg is recovering one of his couch cushions. The cushion is in the shape of a rectangular prism. Greg drew a net of the cushion below.
Note: Figure is not drawn to scale.
If the length of the cushion measures 13 in, the width measures 7 in, and the height measures 4 in, how much fabric does Greg need to cover the cushion?
To find the surface area of the cushion, we need to find the area of each of the six faces and then add them all together.
1. The front face and the back face are both rectangles with dimensions 13 in by 4 in. The area of one of these faces is 13 in * 4 in = 52 sq in. Since there are two of these faces, the total area for both is 2 * 52 sq in = 104 sq in.
2. The top face and the bottom face are also rectangles with dimensions 13 in by 7 in. The area of one of these faces is 13 in * 7 in = 91 sq in. Since there are two of these faces, the total area for both is 2 * 91 sq in = 182 sq in.
3. The left side face and the right side face are rectangles with dimensions 7 in by 4 in. The area of one of these faces is 7 in * 4 in = 28 sq in. Since there are two of these faces, the total area for both is 2 * 28 sq in = 56 sq in.
Adding up the areas of all six faces gives a total surface area of 104 sq in + 182 sq in + 56 sq in = 342 sq in.
Therefore, Greg needs 342 sq in of fabric to cover the cushion.