Emma is interested in finding the formula for the area of a circle. She has studied how to find the circumference
of a circle and knows the formula . She has seen a picture of a series of concentric circles and wants to use
that to work out the area of a circle. She has a series of circular rings made of string and organizes them as seen in the
given picture. She then cuts them at a single point and places them, keeping the distances between the rings the same
as they were in the circle, to form the triangle shown.
What can be said about the radius of the orginal circle and the height of the triangle?
The base of the triangle must be equal to the circumference of the circle. If the circle has radius , what is the
length of the base of the triangle?
In terms of and , work out the area of the triangle. Fully simplify your result.
After this experiment, what formula do you think Emma decided to use to work out the area of a circle?