Mission Top Ten

To solve this problem, we need to find the area of the black shaded region.

First, we will find the area of the square shape. Since the four circles with equal radius $r$, touch each other by their edges, we can form a square from the centers of these circles. The side length of the square is equal to the diameter of a circle, $2 \times r$. Therefore, the area of the square is, $(2 \times r)^2$.

Now, if we can find the area of a quarter circle, we can subtract it from the square area four times.

The area of a quarter circle is, $( \pi \times r^2 ) \div 4$.