To determine the area of a triangle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 13 yards and the height is 5 yards.
Substituting the values into the formula:
\[ \text{Area} = \frac{1}{2} \times 13 \times 5 \]
Calculating this gives:
\[ \text{Area} = \frac{1}{2} \times 65 = 32.5 \text{ square yards} \]
Therefore, the area of the triangle is 32.5 square yards.
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