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[edit] Centroids Of Common Shapes Of Areas And Lines

[edit] Triangular Area

$Area = \frac {b*h}{2}$

[edit] Quarter Circular Area

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

[edit] Semicircular Area

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

[edit] Semiparabolic Area

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

[edit] Parabolic Area

$Area = \frac {4ah}{3}$

[edit] Parabolic Spandrel

$Area = \frac {ah}{3}$

[edit] Circular Sector

$Area = \alpha\ r^2$

[edit] Quarter Circular Arc

$Area = \frac { \pi\ }{2}$

[edit] Semi Circular Arc

$Area = \pi\ r$

[edit] Arc Of Circle

$Area = 2 \alpha\ r$

[edit] Moments Of Inertia of Common Geometric Shapes

[edit] Rectangle

$I = \frac {b h^3}{12}$

[edit] Triangle

[edit] Circle

$I = \frac { \pi\ r^4}{4}$

[edit] 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

[edit] Semicircle

[edit] Quarter Circle

[edit] Ellipse

Statics/Geometric Properties of Lines and Areas