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.
Crescents and Triangles
Stage: 4 Challenge Level:
Triangle ABC is right angled at A and semi circles are drawn on
all three sides producing two 'crescents'.
Show that the sum of the areas of the two crescents equals the
area of triangle ABC.
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. More information on many of our other activities
can be found here.