Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The area of the left rectangle is 48 square inches. The area of the middle rectangle is 64 square inches, and the area of the rectangle on the right is 80 square inches. Two right triangles adjoin the middle rectangle at the top and bottom, with its perpendicular side measuring 6 inches and the common base side marked with a question mark.
Given the following net, what is the area of the triangular base?
(1 point)
Responses
8 inches
8 inches
10 inches
10 inches
24 in.2
24 in. squared
48 in.2
48 in. squared
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24 in. squared
To find the area of the triangular base, we need to calculate the area of the entire rectangle that surrounds the triangular base. The left rectangle has an area of 48 square inches, the middle rectangle (which includes the base) has an area of 64 square inches, and the right rectangle has an area of 80 square inches.
By subtracting the area of the left and right rectangles from the area of the entire rectangle, we can determine the area of the triangular base:
64 (middle rectangle) - 48 (left rectangle) - 80 (right rectangle) = 64 - 48 - 80 = 64 - 128 = -64
Since we cannot have a negative area, we know there was a calculation mistake. We subtracted the area of the left rectangle when we should have added it because we need the total area of the middle rectangle which includes the left rectangle as well. Let's correct the calculation:
64 (middle rectangle) + 48 (left rectangle) + 80 (right rectangle) = 64 + 48 + 80 = 192 in. squared
Now, the total area of the entire rectangle that includes the triangular base is 192 square inches.
Since the triangular base makes up half of the middle rectangle, we divide the total area of the middle rectangle (192 in. squared) by 2:
192 (total area) / 2 = 96 in. squared
Therefore, the area of the triangular base is 96 square inches.