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?

Bound to Be

Age 14 to 16 Challenge Level

$ABCD$ is a square of side 1 unit.
Arc of circles with centres at $A, B, C, D$ are drawn in.

Prove that the area of the central region bounded by the four
arcs is: