What is the area of a shaded region in the quarter circle
radius 12

I guess that the shaded area is a quarter of a circle of radius 12 units.

Is easy to know that the area, will be equal to the quotient between the area of a circle of radius 12, and 4

We know that the area of a circle of radius R is:

A = pi*R^2

in this case, R = 12

pi = 3.14

Then:

A = 3.14*12^2 = 452.16

And a fourth of that is:

A/4 = (452.16)/4 = 113.04

The area of the shaded region is 113.04 square units