Apoint is chosen at random in a large square what percent of the time will the point be in the shaded region

  84.5%

Step-by-step explanation:

The area of the smaller square is ...

  smaller square = (5.98 cm)^2 = 35.7604 cm^2

The area of the larger square is ...

  larger square = (15.2 cm)^2 = 231.04 cm^2

So, the shaded area is ...

  larger square - smaller square = (231.04 -35.7604) cm^2 = 195.2796 cm^2

Then a randomly chosen point will be in the shaded region this fraction of the time:

  (shaded area)/(larger square area) = 195.2796/231.04 ≈ 0.84522 ≈ 84.5%