this puzzle by Peter Grabarchuk appears on the 'Mathsisfun' website as 'double hearts ratio'
a square with semicircles
which area is larger
the gold yellow
this could be posed with a grid as a simple 'area of a circle' question
inviting students to make an initial estimate of which looks larger
however it is more challenging to pose the problem without a grid
various relationships are not too difficult to establish
what is the relationship between
R and r?
then the areas (in the right angled triangle version) are: