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.
Diagonals for Area
Age 14 to 16 Challenge Level:
Prove that the area of a quadrilateral is given by half the
product of the lengths of the diagonals multiplied by the sine of
the angle between the diagonals.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.