04 Four overlapping semi-circles inside a square Jhun Vert Fri, 05/01/2020 - 09:30 pm

Example 04
The figure shown below consists of arcs of four semi-circles with centers at the midpoints of the sides of a square. The square measures 20 cm by 20 cm. Find the area bounded by these circular arcs shaded in the figure shown.
 

Overlapping semi-circular arcs

 

03 Area enclosed by pairs of overlapping quarter circles Jhun Vert Fri, 05/01/2020 - 09:25 pm

Example 03
The shaded regions in the figure below are areas bounded by two circular arcs. The arcs have center at the corners of the square and radii equal to the length of the sides. Calculate the area of the shaded region.
 

02 Area bounded by arcs of quarter circles Jhun Vert Fri, 05/01/2020 - 09:16 pm

Example 02
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.
 

Area common to four quarter circles

 

01 Arcs of quarter circles Jhun Vert Fri, 05/01/2020 - 05:10 pm

Example 01
The figure shown below are circular arcs with center at each corner of the square and radius equal to the side of the square. It is desired to find the area enclosed by these arcs. Determine the area of the shaded region.
 

Intersection area of circular quadrants