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
48 in.2
, 48 in. squared
10 inches
10 inches
8 inches
8 inches
24 in.2
We can see from the net that the triangular base is made up of the right triangles with a perpendicular side of 6 inches and a base that we need to find. Since the area of the middle rectangle is 64 square inches, we know that its base times its height must equal 64. We also know that the base of the middle rectangle plus the two bases of the side rectangles must equal the perimeter of the triangular base. The perimeter of the triangular base can be found by adding the lengths of the three sides: 6 + 8 + x, where x is the unknown side length. Setting this equal to the sum of the rectangles' bases, we get:
6 + 8 + x = 16 + 12
x = 10
Therefore, the area of the triangular base is:
(1/2) * 6 * 10 = 30 square inches
Answer: 30 in.2