To find the surface area of the triangular prism, we need to calculate the area of the two triangular bases and the three rectangular lateral faces.
Step 1: Calculate the area of the triangular base.
The formula for the area \( A \) of a triangle is: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, the base of the triangle is 16 meters and the height is 15 meters.
\[ A = \frac{1}{2} \times 16 \times 15 = \frac{1}{2} \times 240 = 120 \text{ square meters} \]
Since the prism has two triangular bases, the total area of the triangular bases is: \[ \text{Area of two bases} = 2 \times 120 = 240 \text{ square meters} \]
Step 2: Calculate the area of the rectangular lateral faces.
The prism has three rectangular faces. We can find the area of each face:
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Rectangular Face 1 (base of 16 meters and height 11 meters): \[ \text{Area} = 16 \times 11 = 176 \text{ square meters} \]
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Rectangular Face 2 (one side of the triangle which is 17 meters and height 11 meters): \[ \text{Area} = 17 \times 11 = 187 \text{ square meters} \]
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Rectangular Face 3 (the other side of the triangle which is also 17 meters and height 11 meters): \[ \text{Area} = 17 \times 11 = 187 \text{ square meters} \]
Adding up the areas of the rectangular faces: \[ \text{Total area of rectangular faces} = 176 + 187 + 187 = 550 \text{ square meters} \]
Step 3: Calculate the total surface area of the prism.
The total surface area \( S \) of the prism is the sum of the area of the triangular bases and the rectangular lateral faces: \[ S = \text{Area of triangular bases} + \text{Area of rectangular faces} \] \[ S = 240 + 550 = 790 \text{ square meters} \]
Therefore, the surface area of the net of the triangular prism is 790 square meters.
The correct response is: 790 square meters.