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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?

Two Shapes & Printer Ink

Age 14 to 16
Challenge Level
Two shapes

If I print this page which shape will require more yellow ink?

Estimate first making a note of your decision and how you made it.

How has this shape been created?

How would you get a reliable calculation for the area that needs yellow ink?

Create shapes of your own that look good.

Challenge yourself to calculate their areas.