The Correct Answer and Explanation is:
The correct answer is 376 square inches.
The question asks for the amount of plastic Terry used to make the birdhouse before cutting the hole. This means we need to calculate the total surface area of the complete rectangular prism.
The birdhouse has the shape of a rectangular prism with three given dimensions: a length of 10 inches, a width of 8 inches, and a height of 6 inches. The total surface area of an object is the sum of the areas of all its individual surfaces. A rectangular prism has six faces, which can be grouped into three pairs of identical rectangles.
To find the total surface area, we can calculate the area of each pair of faces and then add them all together.
- Front and Back Faces: The dimensions of the front face are length and height.
Area of one face = 10 inches × 6 inches = 60 square inches.
Since there are two identical faces (front and back), their combined area is 2 × 60 = 120 square inches. - Top and Bottom Faces: The dimensions of the top face are length and width.
Area of one face = 10 inches × 8 inches = 80 square inches.
Since there are two identical faces (top and bottom), their combined area is 2 × 80 = 160 square inches. - Left and Right Side Faces: The dimensions of the side faces are width and height.
Area of one face = 8 inches × 6 inches = 48 square inches.
Since there are two identical faces (left and right), their combined area is 2 × 48 = 96 square inches.
Finally, to find the total amount of plastic used, we add the areas of all six faces:
Total Surface Area = 120 sq in + 160 sq in + 96 sq in = 376 square inches.
Therefore, Terry used 376 square inches of plastic to build the birdhouse before the hole was made.
