To calculate the surface area of the net of the triangular prism, we need to find the areas of the two triangular bases and the three rectangular lateral faces.
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Area of the triangular base: The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangular base, the base measures 16 meters and the height is 15 meters: \[ A = \frac{1}{2} \times 16 \times 15 = 120 \text{ square meters} \]
Since there are two triangular bases: \[ \text{Total area of triangular bases} = 2 \times 120 = 240 \text{ square meters} \]
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Areas of the rectangular faces:
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The first rectangular face is the one connected to the triangular base with dimensions \( 11 \text{ meters (width)} \times 16 \text{ meters (base length)} \): \[ A_1 = 11 \times 16 = 176 \text{ square meters} \]
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The second rectangular face corresponds to one of the triangular sides with dimensions \( 11 \text{ meters (width)} \times 17 \text{ meters (triangle side length)} \): \[ A_2 = 11 \times 17 = 187 \text{ square meters} \]
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The third rectangular face corresponds to the other triangular side, which also measures \( 11 \text{ meters (width)} \times 17 \text{ meters (same triangle side length)} \): \[ A_3 = 11 \times 17 = 187 \text{ square meters} \]
Now we combine the areas of all rectangular faces: \[ \text{Total area of rectangular faces} = A_1 + A_2 + A_3 = 176 + 187 + 187 = 550 \text{ square meters} \]
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Total surface area of the prism: Now we can find the total surface area \( S \) by adding the area of the triangular bases and the rectangular faces: \[ S = \text{Total area of triangular bases} + \text{Total area of rectangular faces} = 240 + 550 = 790 \text{ square meters} \]
So, the surface area of the net of the triangular prism is 790 square meters.