The area of the shaded region is about 17.38 squared meters.
The shape with a square with four 1/4 of a circle on each corner, which form the diamond-like shaded shape. So to find the area of the shaped shape, subtract four 1/4 of a circle by the square.
Circle: (1/4 • 4 = 1)
A = πr • r
π 4.5 • 4.5
A ≈ 63.62
Square:
A = s • s
9 • 9
A = 81
81 - 63.62 = 17.38