To find the surface area of the triangular prism, we need to calculate the area of the triangular base and the area of the three rectangular faces.
Step 1: Calculate the area of the triangular base.
The formula for the area of a triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of the triangle is 5 yards and the height (which is also the left side of the triangle since it forms a right angle with the base) is 12 yards.
\[ \text{Area} = \frac{1}{2} \times 5 \times 12 = \frac{1}{2} \times 60 = 30 \text{ square yards} \]
Step 2: Calculate the area of the three rectangular faces.
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Rectangular face from the left side of the triangle (12 yards): \[ \text{Area} = \text{height} \times \text{length} = 12 \times 11 = 132 \text{ square yards} \]
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Rectangular face from the base of the triangle (5 yards): \[ \text{Area} = 5 \times 11 = 55 \text{ square yards} \]
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Rectangular face from the hypotenuse of the triangle (13 yards): \[ \text{Area} = 13 \times 11 = 143 \text{ square yards} \]
Step 3: Add all the areas together.
- Area of triangular base: \(30\) square yards
- Area of rectangular face (12 yards): \(132\) square yards
- Area of rectangular face (5 yards): \(55\) square yards
- Area of rectangular face (13 yards): \(143\) square yards
Adding these areas together: \[ \text{Total Surface Area} = 30 + 132 + 55 + 143 = 360 \text{ square yards} \]
Conclusion
The surface area of the triangular prism is \(360\) square yards. Therefore, the correct response is:
360 square yards