Answer: 414 square yards
========================================================
Explanation:
Surround the entire figure in a bounding rectangle as shown below.
This surrounding rectangle is 23 by 27. It's total area is 23*27 = 621 square yards.
For a moment, let's ignore the 3x3 section marked in the dashed lines. The empty space in the bottom left corner is 15+3 = 18 by 9+3 = 12. Its area is 18*12 = 216 square yards. Accounting for the dash line 3x3 section means we subtract 9 from the 216 to get 216-9 = 207. The empty space takes up 207 square yards.
So the purple region must take up 621-207 = 414 square yards
