quarter circle

Problem
Arcs of quarter circles are drawn inside the square. The center of each circle is at each corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20 cm. Find the area common to the four circular quadrants. See figure below.
 

Problem
The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.
 

Problem 724
Find the coordinates of the centroid of the shaded area shown in Fig. P-724.
 

Problem 723
Locate the centroid of the shaded area in Fig. P-723.
 

Problem 722
Locate the centroid of the shaded area in Fig. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r.
 

Problem 706
Determine the centroid of the quarter circle shown in Fig. P-706 whose radius is r.