Question

In the square below the four quarter circles are congruent. find the area of the shaded region.

Answer 1

The quarter circle pieces are all congruent allowing us to glue them together to form a circle. The circle will be completely inside the square. This circle is as large as possible so it's not spilling outside of the square. 

The area of the square is 8*8 = 64 square units

The circle has a radius of 8/2 = 4 units. Use r = 4 and plug this into the area of a circle formula
A = pi*r^2
A = pi*4^2
A = pi*16
A = 16pi

Now subtract the two areas
(area of square) - (area of circle) = 64 - 16pi

The exact answer, in terms of pi, is 64 - 16pi

If your teacher wants you to find the approximate decimal version, then you would use a calculator to find that 64 - 16pi = 13.7345175 approximately. If you end up going with the approximate answer, be sure to follow the instructions on what your teacher wants with rounding.