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
24 in.²
To find the area of the triangular base, we first need to calculate the height of the triangle. The height is the side length of the rectangles, which is 6 inches.
Since the area of a triangle is 1/2 * base * height, we can substitute the values into the formula:
Area = 1/2 * base * height
Area = 1/2 * x * 6
Area = 3x
Now we know that the area is equal to 24 in², so:
3x = 24
x = 8
Therefore, the base of the triangle is 8 inches. To find the area of the triangle, we can use the formula:
Area = 1/2 * base * height
Area = 1/2 * 8 * 6
Area = 24 in²
So the area of the triangular base is 24 in².