To find the actual area of the triangular park in square yards, we first need to calculate the area of the triangle using the dimensions given in the map, and then convert those dimensions from inches to yards using the provided scale.
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Calculate the area of the triangle on the map: The formula for the area \( A \) of a triangle is given by:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base of the triangle on the map is 3 inches, and the height is 2 inches:
\[ A = \frac{1}{2} \times 3 , \text{inches} \times 2 , \text{inches} = \frac{1}{2} \times 6 , \text{square inches} = 3 , \text{square inches} \]
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Convert the area from square inches to square yards: Next, we need to convert the dimensions from inches to yards. Given the scale of 1 inch = 20 yards, we can convert square inches to square yards as follows:
\[ 1 , \text{inch} = 20 , \text{yards} \implies 1 , \text{square inch} = (20 , \text{yards})^2 = 400 , \text{square yards} \]
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Calculate the actual area in square yards: Now, we convert the area calculated in square inches to square yards:
\[ A_{\text{actual}} = 3 , \text{square inches} \times 400 , \text{square yards per square inch} \]
\[ A_{\text{actual}} = 1200 , \text{square yards} \]
Therefore, the actual area of the park is
\[ \boxed{1200} \text{ square yards}. \]