Area of a Circle by Lines

Have a look at this:


You get a triangle! And it's area is:

Area = base × height / 2

Area = 2πr × r / 2

Area = πr2


Area of Circle = πr2

Also notice:

Circumference of 2πr  →  Area of πr2

Things to Try

Try a low value for "sides":

Also try increasing the value of "lines" to convince yourself that the lines are heading towards filling the whole area.