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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).


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.

Get Cross

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?

Triangles and Petals

Age 14 to 16
Challenge Level
Sketch a diagram and write on all the angles you know, and work out any angles you can find. Once you know the angle at the centre of the sectors, you can work out the proportion of the circle's circumference for each petal.