Find the area \( A \). Write your answer in exact simplest form. \[ A=\frac{1}{2} b h \text { for } b=\frac{2}{5} \text { yd and } h=\frac{5}{9} \text { yd (area of a triangle) } \]

To find the area \( A \) of the triangle using the formula \( A = \frac{1}{2} b h \), we can substitute the given values. Here, the base \( b = \frac{2}{5} \) yd and the height \( h = \frac{5}{9} \) yd. Substituting these values into the formula, we get: \[ A = \frac{1}{2} \left(\frac{2}{5}\right) \left(\frac{5}{9}\right) \] Now, multiplying the values: \[ A = \frac{1}{2} \cdot \frac{2 \cdot 5}{5 \cdot 9} = \frac{1}{2} \cdot \frac{10}{45} = \frac{10}{90} \] This simplifies to: \[ A = \frac{1}{9} \text{ yd}^2 \] Thus, the area \( A \) in exact simplest form is: \[ A = \frac{1}{9} \text{ yd}^2 \]