Centroids of regular-shape areas

Shape	Figure			Area
Triangular Area		$Description: \frac{b}{3}$	$Description: \frac{h}{3}$	$Description: \frac{bh}{2}$
Quarter-circular area		$Description: \frac{4r}{3\pi}$	$Description: \frac{4r}{3\pi}$	$Description: \frac{\pi r^2}{4}$
Semicircular area		$Description: \,\!0$	$Description: \frac{4r}{3\pi}$	$Description: \frac{\pi r^2}{2}$
Quarter-elliptical area		$Description: \frac{4a}{3\pi}$	$Description: \frac{4b}{3\pi}$	$Description: \frac{\pi a b}{4}$
Semi- parabolic area		$Description: \,\!0$	$Description: \frac{4b}{3\pi}$	$Description: \frac{\pi a b}{2}$