Area in a Square
Bounded by
Quarter-Circle Arcs

Given a square, construct a region in the center that is bounded by the four quarter-circle arcs using the vertices as centers and sides of the square as radius.

Find the area of that center region -- the yellow region in the figure at the right --  for a square with side length  s.






Hint:    There are three different shapes in the square -- yellow, pink, and blue. If we add the areas of  each of the four Quarter-Circles  we get an area that is equivalent to  4 yellow, 12 pink and 8 blue.   Now  3 yellow + 12 Pink + 12 blue would be 3 squares

So the area of   1 yellow is  the total of 4 quarter-circles - 3 squares + 4 blues.   Try to find an expression for one of the blue sections in terms of   s.




Return to EMAT 4600/6600 Page