To find the surface area of the triangular prism, we need to calculate the area of its three rectangular faces and the area of the two triangular bases.
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Area of the triangular base: The formula for the area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).
Given the base measures 16 meters and the height measures 15 meters:
\[ \text{Area of one triangular base} = \frac{1}{2} \times 16 \times 15 = 120 \text{ square meters} \]Since there are two identical triangular bases, the total area of the two bases is:
\[ 2 \times 120 = 240 \text{ square meters} \] -
Area of the rectangular faces:
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Base Rectangle: The width of the prism is given as 11 meters and the length is the same as the side of the triangle, which is 16 meters. \[ \text{Area of the base rectangle} = 16 \times 11 = 176 \text{ square meters} \]
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Right Rectangular Face: This face has a width of 11 meters and a height corresponding to the length of the triangle sides (17 meters). \[ \text{Area of the right rectangle} = 17 \times 11 = 187 \text{ square meters} \]
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Left Rectangular Face: This also has the same dimensions as the right rectangular face. \[ \text{Area of the left rectangle} = 17 \times 11 = 187 \text{ square meters} \]
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Total Area of the Rectangular Faces: Adding the areas of all three rectangular faces:
\[ \text{Total area of rectangular faces} = 176 + 187 + 187 = 550 \text{ square meters} \] -
Total Surface Area of the Prism: Adding the area of the triangular bases to the area of the rectangular faces: \[ \text{Total surface area} = 240 + 550 = 790 \text{ square meters} \]
Thus, the surface area of the net of the triangular prism is 790 square meters.
So the correct response is 790 square meters.