To solve the equation
\[ \frac{4}{5} a = 11, \]
we will isolate \(a\) by multiplying both sides by the reciprocal of \(\frac{4}{5}\), which is \(\frac{5}{4}\).
\[ a = 11 \times \frac{5}{4} \]
Now calculate the right side:
\[ a = \frac{11 \times 5}{4} = \frac{55}{4} \]
Thus, the simplified answer is
\[ a = \frac{55}{4}. \]