P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?
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).
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.