Hans Georg Schaathun
Mars 2016
$$A_T = \frac{|AB|\cdot h}{2}$$
$$A_P = nA_T = \frac{n\cdot|AB|\cdot h}{2}$$
$$\lim_{n\to\infty} h = r$$
$$\lim_{n\to\infty} n|AB| = 2\pi r$$
$$A_S = \lim_{n\to\infty} A_P = \frac{2\pi r\cdot r}{2} = \pi r^2$$
