Area of a Circle by Lines

Have a look at this:

 

A circle becomes a triangle! And the area is:

Area = base × height / 2

Area = 2πr × r / 2

Area = πr2

Conclusion

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.