how do i find the probability that a point in a figue lies in the shaded region, when the figure is a circle with an inscribed square? the circle has a radius of 2 and is also the shaded region the square has a radius of the square root of two.

Answer 1

Since when does a square have a radius? If this is the distance from the center of the circle to a corner of the "inscribed square" touching the perimeter circle, it would seem that it would have a radius with the same value of that of the circle.

Whatever that value, the diameter (2r) would be the diagonal from one corner of the square to the other. From this value, use the Pythagorean theorem to determine the value of the sides of the square.

Calculate the areas of both the square and the circle. Divide the area of the square by the area of the circle.

I hope this helps. Thanks for asking.