Use the image to answer the question.
A net of a triangular prism is drawn unfolded and open. It shows a dashed line equilateral triangle in the center, with 3 triangles adjoined to the baselines of the central triangle.
A baseline of the central triangle is labeled as 17 feet. The perpendicular height of the central base triangle is 14.7 feet, drawn with a dotted line and a right angle symbol with the base. The perpendicular height of an adjoined triangle is shown as 13.8 feet, and is drawn with a dotted line and a right angle symbol with the base.
Find the surface area of a triangular pyramid represented by the given net.
(1 point)
ft.2
The formula for finding the surface area of a triangular prism is:
Surface Area = 2(base area of the triangle) + (perimeter of the triangle) * (height of the prism)
First, we need to find the base area of the central triangle:
Base area = (1/2) * base * height
Base area = (1/2) * 17 * 14.7
Base area = 124.95 ft^2
Next, we need to find the perimeter of the central triangle:
Perimeter = 3 * base
Perimeter = 3 * 17
Perimeter = 51 ft
Now we can find the surface area of the triangular prism:
Surface Area = 2(124.95) + 51 * (13.8)
Surface Area = 249.9 + 703.8
Surface Area = 953.7 ft^2
Therefore, the surface area of the triangular prism represented by the given net is 953.7 ft^2.