Area of circle outside of the square


In the diagram the circle and square have the same centre and the same perimeter. What fraction of the area of square lies outside the circle? What fraction of the area of circle lies outside the square?

Area of circle outside of the square

Area of circle outside of square solution

Problem Page Coordinator: Stephen Lee CMath MIMA
Mathematics in Education and Industry
Acknowledgement: The IMA are indebted to MEI for sourcing and supplying Mathematics Today with these well-known puzzles.
First published in Mathematics Today (December 2014)
Published