Let $A$ be the area of the locus of points $z$ in the complex plane that satisfy $|z+12+9i| \leq 15$.  Compute $\lfloor A\rfloor$.
1. The given problem involves finding the area of the locus of points \( z \) in the complex plane that satisfy \( |z + 12 + 9i| \leq 15 \). This represents a circle in the complex plane.

2. The general form of a circle in the complex plane is \( |z - z_0| \leq r \), where \( z_0 \) is the center of the circle and \( r \) is the radius. In this case, we can rewrite the given inequality as:
   \[
   |z + 12 + 9i| \leq 15
   \]
   This can be interpreted as a circle with center at \( -12 - 9i \) and radius \( 15 \).

3. To find the area \( A \) of this circle, we use the formula for the area of a circle:
   \[
   A = \pi r^2
   \]
   Here, the radius \( r \) is \( 15 \). Therefore, the area \( A \) is:
   \[
   A = \pi \times 15^2 = \pi \times 225 = 225\pi
   \]

4. We need to compute the integer part of this area, which is \( \lfloor A \rfloor \). Using the approximation \( \pi \approx 3.14159 \), we get:
   \[
   A \approx 225 \times 3.14159 = 706.85775
   \]

5. The integer part of \( 706.85775 \) is \( 706 \).

Conclusion:
\[
\lfloor A \rfloor = 706
\]

The final answer is \( \boxed{ 706 } \)