To find the surface area of the net of the triangular prism, we need to calculate the area of the triangular bases and the rectangular lateral faces.
1. Area of the triangular face:
The triangle has sides measuring 17m, 17m, and 16m. First, we can find the area of the triangle using Heron's formula.
- Compute the semi-perimeter \( s \): \[ s = \frac{a + b + c}{2} = \frac{17 + 17 + 16}{2} = 25 \text{ m} \]
- The area \( A \) of the triangle is given by: \[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Where \( a = 17 \), \( b = 17 \), and \( c = 16 \).
Calculating the individual terms: \[ s - a = 25 - 17 = 8 \] \[ s - b = 25 - 17 = 8 \] \[ s - c = 25 - 16 = 9 \]
Now calculate the area: \[ A = \sqrt{25 \times 8 \times 8 \times 9} \] \[ A = \sqrt{14400} \] \[ A = 120 \text{ sq m} \]
Since there are two triangular faces, the total area of the triangular faces is: \[ \text{Total area of triangular faces} = 2 \times 120 = 240 \text{ sq m} \]
2. Area of the rectangular lateral faces:
The prism has three rectangular faces, each corresponding to the sides of the triangular face:
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Two rectangular faces corresponding to the equal sides (17m): \[ \text{Area of each} = \text{height} \times \text{width} = 17 \times 11 = 187 \text{ sq m} \] Thus, for two faces: \[ 2 \times 187 = 374 \text{ sq m} \]
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One rectangular face corresponding to the base (16m): \[ \text{Area} = 16 \times 11 = 176 \text{ sq m} \]
3. Total surface area calculation:
Adding all the areas together: \[ \text{Total Surface Area} = \text{Area of triangular faces} + \text{Area of rectangular faces} \] \[ = 240 + 374 + 176 = 790 \text{ sq m} \]
Thus, the total surface area of the net of the triangular prism is: \[ \boxed{790 \text{ sq m}} \]
The answer is choice C. 790 sq m.