To find the surface area of the triangular prism, we need to calculate the area of the triangular base and the area of the three rectangular faces.
-
Area of the triangular base: The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base is 16 meters and the height is 15 meters: \[ \text{Area} = \frac{1}{2} \times 16 \times 15 = 120 \text{ square meters} \]
-
Perimeter of the triangular base: The perimeter \( P \) of the triangle is the sum of the lengths of all sides: \[ P = 16 + 17 + 17 = 50 \text{ meters} \]
-
Area of the rectangular faces: The prism has 3 rectangular faces:
- Two face rectangles with dimensions \( 17 \times 11 \)
- One face rectangle with dimensions \( 16 \times 11 \)
Area of the two rectangular faces (height = 17 meters): \[ \text{Area} = 2 \times (17 \times 11) = 2 \times 187 = 374 \text{ square meters} \]
Area of the third rectangular face (base = 16 meters): \[ \text{Area} = 16 \times 11 = 176 \text{ square meters} \]
Total area of the rectangular faces: \[ 374 + 176 = 550 \text{ square meters} \]
-
Total surface area: Finally, the total surface area \( SA \) of the prism is the sum of the area of the triangular bases (which appear at the top and bottom, so we multiply by 2) and the area of the rectangular sides: \[ SA = 2 \times \text{Area of triangle} + \text{Area of rectangles} \] \[ SA = 2 \times 120 + 550 = 240 + 550 = 790 \text{ square meters} \]
Therefore, the surface area of the net of the triangular prism is 790 square meters.
Final Answer: 790 square meters.