Given a square ABCD of sides 10 cm, and using the corners as
centres, construct four quadrants with radius 10 cm each inside the
square. The four arcs intersect at P, Q, R and S. Find the area
enclosed by PQRS.

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Two Circles

Age 14 to 16 Challenge Level:

Draw two circles, each of radius $1$ unit, so that each circle
goes through the centre of the other one. What is the area of the
overlap?