To find the area \( A \) of a trapezoid, we can use the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides, and \( h \) is the height (the distance between the parallel sides).
In this case, the lengths of the parallel sides are \( b_1 = 15 , \text{yd} \) and \( b_2 = 19 , \text{yd} \), and the height \( h = 12 , \text{yd} \).
Plugging these values into the formula:
\[ A = \frac{1}{2} \times (15 + 19) \times 12 \]
Calculating the sum of the bases:
\[ 15 + 19 = 34 \]
Now, substituting this value into the area formula:
\[ A = \frac{1}{2} \times 34 \times 12 \]
Calculating \( \frac{1}{2} \times 34 \):
\[ \frac{1}{2} \times 34 = 17 \]
Now, multiplying by the height:
\[ A = 17 \times 12 = 204 \]
Thus, the area of the trapezoid is
\[ \boxed{204} , \text{yd}^2 \]