In rectangle ABCD, points E and F are on BC and AB, respectively, such
that areas of triangles AFD, FBE, and ECD are all equal to 1. What is
the area of triangle FDE?

Four points A, B, C, and D
lie on a straight line in the X-Y plane, such that AB = BC = CD,
and the length of AB is 1 metre. An ant at A wants to reach a
sugar particle at D. But there are insect repellents kept at points B
and C. The ant would not go within one metre of any insect repellent.
The minimum distance in metres the ant must traverse to reach the sugar
particle is?

Two identical circles intersect so that their centres, and the points
at which they intersect, form a square of side 1 cm. The area in sq. cm
of the portion that is common to the two circles is?