Area - circles, sectors and segments

What is the total area enclosed by the three semicicles?

Weekly Problem 13 - 2006
If three runners run at the same constant speed around the race tracks, in which order do they finish?

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?

Can you maximise the area available to a grazing goat?

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

Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

Can you find a relationship between the area of the crescents and the area of the triangle?

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?