You may also like

problem icon

Giant Holly Leaf

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

problem icon

Quadarc

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.

problem icon

Two Circles

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?

Bound to Be

Age 14 to 16 Challenge Level:

Bounded area $ABCD$ 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:

$(1 + \pi/3 + \sqrt{3})$ square units.

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.
Copyright © 1997 - 2018. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.