How to break this apart?

Question

A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use . =3.14

Answer 1

Make a figure to clarify ideas...but the problem comes down to this.

The area of the playground is 109² =11881.

The 4 skating rinks in area are the same as a circle of area πr².

The area of non-skating rink portion is 9055 which makes the area of the circle = 11881-9055=2826.

The radius of the circle (and thus of each straight side of the skating rink) is sqrt(2826/π).

You can do the arithmetic and since already know the area of the skating rinks, you can easily compute the cost of the concrete.