# 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

$I_{x}=I_{y}={\frac {1}{16}}\pi \ r^{4}$

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