To find the surface area of the net of the triangular prism, we first need to determine the area of the triangular base and the areas of the rectangular faces.
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Area of the Triangular Base: The area \(A\) of a triangle can be calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of the triangle is 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 faces, the total area of both triangular faces is: \[ 2 \times 120 = 240 \text{ square meters} \]
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Area of the Rectangular Faces: There are three rectangular faces. We need to find the area of each.
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Face 1: The base of the triangle (16 meters) times the width of the prism (11 meters): \[ A_1 = 16 \times 11 = 176 \text{ square meters} \]
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Face 2: One side of the triangle (17 meters) times the width of the prism (11 meters): \[ A_2 = 17 \times 11 = 187 \text{ square meters} \]
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Face 3: The other side of the triangle (17 meters) times the width of the prism (11 meters): \[ A_3 = 17 \times 11 = 187 \text{ square meters} \]
Now, add the areas of the three rectangular faces: \[ A_{\text{rectangles}} = A_1 + A_2 + A_3 = 176 + 187 + 187 = 550 \text{ square meters} \]
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Total Surface Area: Now combine the areas of the triangular and rectangular faces: \[ \text{Total Surface Area} = \text{Area of Triangles} + \text{Area of Rectangles} = 240 + 550 = 790 \text{ square meters} \]
So the final answer is:
790 square meters.