The shape is 17 m 15 m 17 m 11 m 16 m What is the surface area of the net of the triangular prism?
(1 point)
A. 790 square meters
B. 779 square meters
C. 822 square meters
D. 768 square meters
To find the surface area of the net of the triangular prism, first calculate the area of each shape that makes up the net:
1. Base: The base of the prism is a triangle with side lengths of 17 m, 15 m, and 16 m. Use Heron's formula to calculate the area of this triangle:
s = (17 + 15 + 16) / 2 = 24
area = sqrt(24(24-17)(24-15)(24-16)) = 120 m^2
2. The lateral surface area consists of three rectangles:
- Rectangle 1: 17 m x 11 m = 187 m^2
- Rectangle 2: 15 m x 11 m = 165 m^2
- Rectangle 3: 16 m x 11 m = 176 m^2
Total lateral surface area = 187 + 165 + 176 = 528 m^2
Now, calculate the total surface area by adding the base area and the lateral surface area:
Total surface area = 120 + 528 = 648 m^2
Therefore, the surface area of the net of the triangular prism is 648 square meters.
Since none of the provided options are correct, it might be necessary to recheck the calculations.