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# Center of area of ​​geometric figures

A click on the respective picture leads to the calculation of the centroids:

General information and exercises for calculating centroids can be found under the respective keyword.

## Centers of area in the plane

### Triangle

$y_S = \frac{h}{3}$

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### Parallelogram

$y_S = \frac{h}{2}$

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### Trapezoid

$y_S = \frac{h}{3} \cdot \frac{a+2\cdot b}{a+b}$

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### Circle section

$y_S = \frac{2 \cdot r \cdot sin \alpha}{3 \cdot \alpha}$

$y_S = \frac{2 \cdot r \cdot l}{3 \cdot b}$

For the semicircle it is

$y_S = \frac{4 \cdot r }{3 \cdot \pi}$

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### Circle segment

$y_S = \frac{2}{3} \cdot \frac{r \cdot sin^3 \alpha}{\alpha -- sin \alpha \cdot cos \alpha}$

For the semicircle it is

$y_S = \frac{4 \cdot r }{3 \cdot \pi}$

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### Circular ring section

$y_S = \frac{2}{3} \cdot \frac{\left( r_a^3-r_i^3 \right) \cdot sin \alpha}{\left( r_a^2-r_i^2\right) \cdot \alpha}$

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### Parabolic surfaces

Centroid S1

$x_{S1} = \frac{3 \cdot a}{8}$

$y_{S1} = \frac{2 \cdot h}{5}$

Centroid S2

$x_{S2} = \frac{3 \cdot a}{4}$

$y_{S2} = \frac{3 \cdot h}{10}$

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### Parabolic section

$y_S = \frac{2 \cdot h}{5}$

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### Elliptical section

$y_S = \frac{2 }{3} \cdot \frac{b \cdot sin^3 \alpha}{\alpha -- sin \alpha \cdot cos \alpha}$

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