Perimeter and Area

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Where should runners start the 200m race so that they have all run the same distance by the finish?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?