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)
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To find the surface area of the triangular prism represented by the given net, we need to find the surface area of each individual triangle and then add them all together.
The surface area of the central triangle can be calculated using the formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
Area = (sqrt(3)/4) * 17^2
Area = (sqrt(3)/4) * 289
Area = 74.3 square feet
Since there are three identical triangles adjoined to the central triangle, we can calculate the surface area of one of them and then multiply by 3:
Area = (1/2) * base * height
Area = (1/2) * 17 * 13.8
Area = 117.3 square feet
Therefore, the total surface area of the triangular prism represented by the given net is:
74.3 + 117.3 = 191.6 square feet
So, the surface area of the triangular prism is 191.6 square feet.