${\mathrm{Area}}_{\mathrm{polygon}}$

$\=$

$n\cdot \left({\mathrm{Area}}_{\mathrm{triangle}}\right)$

${\mathrm{Area}}_{\mathrm{polygon}}$

$\=$

$n\cdot \left(\frac{b\cdot h}{2}\right)$

${\mathrm{Area}}_{\mathrm{polygon}}$

$\=$

$\frac{1}{2}\cdot h\cdot \left(n\cdot b\right)$

By rearranging the equation $n\cdot b$ represents the perimeter of the polygon. As n increases the perimeter of the polygon approaches the circumference of a circle.

≈

$\frac{1}{2}\cdot r\cdot \left(2\cdot {\mathrm{\π}}_{}\cdot r\right)$

=

${\mathrm{\π}}_{}\cdot r^2$