# Centroids Of Common Shapes Of Areas And Lines

## Triangular Area

$Area={\frac {b*h}{2}}$ ## Quarter Circular Area

$Area={\frac {\pi \ r^{2}}{4}}$ ## Semicircular Area

$Area={\frac {\pi \ r^{2}}{2}}$ ## Semiparabolic Area

$Area={\frac {2ah}{3}}$ ## Parabolic Area

$Area={\frac {4ah}{3}}$ ## Parabolic Spandrel

$Area={\frac {ah}{3}}$ ## Circular Sector

$Area=\alpha \ r^{2}$ ## Quarter Circular Arc

$Area={\frac {\pi \ }{2}}$ ## Semi Circular Arc

$Area=\pi \ r$ ## Arc Of Circle

$Area=2\alpha \ r$ # Area Moments Of Inertia of Common Geometric Shapes

## Rectangle

$I_{x}={\frac {1}{3}}bh^{3}$ $I_{y}={\frac {1}{3}}hb^{3}$ $I_{x'}={\frac {1}{12}}bh^{3}$ $I_{y'}={\frac {1}{12}}hb^{3}$ ## Right Triangular Area

$I_{x}={\frac {1}{12}}bh^{3}$ $I_{y}={\frac {1}{4}}hb^{3}$ $I_{x'}={\frac {1}{36}}bh^{3}$ $I_{y'}={\frac {1}{36}}hb^{3}$ ## Triangular Area

$I_{x}={\frac {1}{12}}bh^{3}$ $I_{x'}={\frac {1}{36}}bh^{3}$ ## Circular Area

$J_{C}={\frac {\pi \ r^{4}}{2}}$ $I_{x'}=I_{y'}={\frac {\pi \ r^{4}}{4}}$ ## Hollow circle

This is used for hollow cylinders where there is solid material between the outer and inner radius, but no material between the inner radius and the center, like a pipe's cross-section.

$I={\frac {\pi \ (r_{o}^{4}-r_{i}^{4})}{4}}$ $r_{o}$ is the outer radius $r_{i}$ is the inner radius

## Semicircular Area

$I_{x}=I_{y}={\frac {1}{8}}\pi \ r^{4}$ $I_{x'}=({\frac {\pi }{8}}-{\frac {8}{9\pi }})r^{4}$ $I_{y'}={\frac {1}{8}}\pi \ r^{4}$ ## Quarter Circle

$I_{x}=I_{y}={\frac {1}{16}}\pi \ r^{4}$ $I_{x'}=I_{y'}=({\frac {\pi }{16}}-{\frac {4}{9\pi }})r^{4}$ 