Area of Circle - Is there an easy way?

Area, Circle


Observe below applet.
Try to find relationship between square edge (TW) size and radius of circle. You can do this by equating areas of circle and square. Did you manage to find one?

Now someone asks you to find the area of a circle of radius 6. Can you find it, without using pi? What will be the area?



Find the area of outermost circle by using the formula you know: pi*r^2 using the value of radius = g. Can you find the area of the same circle by calculating area of corresponding triangle shown?
Change the slider values a to g and try to minimise the error you are observing in trying to find area of actual circle which is not hollow!!!