To find the surface area of the net of the triangular prism, we need to calculate the areas of the triangular bases and the rectangular lateral faces.
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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 of the triangle is 16 meters and the height is 15 meters.
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 16 \times 15 = \frac{1}{2} \times 240 = 120 \text{ square meters} \]
Since there are two triangular bases: \[ \text{Total area of triangle} = 2 \times 120 = 240 \text{ square meters} \]
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Area of the Rectangular Faces: The prism has three rectangular faces. We will calculate the area of each:
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Base Rectangle: The base that connects the two triangular faces is 16 meters in length and has a width of 11 meters (the height of the prism). \[ \text{Area}_{\text{base}} = 16 \times 11 = 176 \text{ square meters} \]
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Left Rectangle: One side of the triangle measures 17 meters, so the area of the left rectangle is: \[ \text{Area}_{\text{left}} = 17 \times 11 = 187 \text{ square meters} \]
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Right Rectangle: The other side of the triangle also measures 17 meters, so the area of the right rectangle is: \[ \text{Area}_{\text{right}} = 17 \times 11 = 187 \text{ square meters} \]
Now, summing up the areas of the rectangular faces: \[ \text{Total area of rectangles} = 176 + 187 + 187 = 550 \text{ square meters} \]
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Total Surface Area of the Prism: By adding the areas of the triangular bases and the rectangular faces: \[ \text{Total Surface Area} = \text{Total area of triangles} + \text{Total area of rectangles} \] \[ \text{Total Surface Area} = 240 + 550 = 790 \text{ square meters} \]
Thus, the surface area of the net of the triangular prism is 790 square meters.