| Shape | Figure | <math>\bar x</math> | <math>\bar y</math> | Area
|
| Triangular area
| Image:Triangle centroid 1.PNG Image:Triangle centroid 2.PNG
|
| <math>\frac{h}{3}</math>
| <math>\frac{bh}{2}</math>
|
| Quarter-circular area
| Image:Quarter-circle-centroid.png
| <math>\frac{4r}{3\pi}</math>
| <math>\frac{4r}{3\pi}</math>
| <math>\frac{\pi r^2}{4}</math>
|
| Semicircular area
| Image:Semicircle-centroid.png
| <math>\frac{}{}0</math>
| <math>\frac{4r}{3\pi}</math>
| <math>\frac{\pi r^2}{2}</math>
|
| Quarter-elliptical area
| Image:Elliptical-quarter.png
| <math>\frac{4a}{3\pi}</math>
| <math>\frac{4b}{3\pi}</math>
| <math>\frac{\pi a b}{4}</math>
|
| Semielliptical area
| The area inside the ellipse <math>\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1</math> and above the <math>\frac{}{}x</math> axis
| <math>\frac{}{}0</math>
| <math>\frac{4b}{3\pi}</math>
| <math>\frac{\pi a b}{2}</math>
|
| Semiparabolic area
| The area between the curve <math>y = \frac{h}{b^2} x^2 </math> and the <math>\frac{}{}y</math> axis, from <math>\frac{}{}x = 0</math> to <math>\frac{}{}x = b</math>
| <math>\frac{3b}{8}</math>
| <math>\frac{3h}{5}</math>
| <math>\frac{2bh}{3}</math>
|
| Parabolic area
| The area between the curve <math>\frac{}{}y = \frac{h}{b^2} x^2 </math> and the line <math>\frac{}{}y = h</math>
| <math>\frac{}{}0</math>
| <math>\frac{3h}{5}</math>
| <math>\frac{4bh}{3}</math>
|
| Parabolic spandrel
| The area between the curve <math>\frac{}{}y = \frac{h}{b^2} x^2 </math> and the <math>\frac{}{}x</math> axis, from <math>\frac{}{}x = 0</math> to <math>\frac{}{}x = b</math>
| <math>\frac{3b}{4}</math>
| <math>\frac{3h}{10}</math>
| <math>\frac{bh}{3}</math>
|
| General spandrel
| The area between the curve <math>y = \frac{h}{b^n} x^n</math> and the <math>\frac{}{}x</math> axis, from <math>\frac{}{}x = 0</math> to <math>\frac{}{}x = b</math>
| <math>\frac{n + 1}{n + 2} b</math>
| <math>\frac{n + 1}{4n + 2} h</math>
| <math>\frac{bh}{n + 1} b</math>
|
| Circular sector
| The area between the curve (in polar coordinates) <math>\frac{}{}r = \rho</math> and the pole, from <math>\frac{}{}\theta = -\alpha</math> to <math>\frac{}{}\theta = \alpha</math>
| <math>\frac{2\rho\sin(\alpha)}{3\alpha}</math>
| <math>\frac{}{}0</math>
| <math>\frac{}{}\alpha \rho^2</math>
|
| Quarter-circular arc
| The points on the circle <math>\frac{}{}x^2 + y^2 = r^2</math> and in the first quadrant
| <math>\frac{2r}{\pi}</math>
| <math>\frac{2r}{\pi}</math>
| <math>\frac{\pi r}{2}</math>
|
| Semicircular arc
| The points on the circle <math>\frac{}{}x^2 + y^2 = r^2</math> and above the <math>\frac{}{}x</math> axis
| <math>\frac{}{}0</math>
| <math>\frac{2r}{\pi}</math>
| <math>\frac{}{}\pi r</math>
|
| Arc of circle
| The points on the curve (in polar coordinates) <math>\frac{}{}r = \rho</math>, from <math>\frac{}{}\theta = -\alpha</math> to <math>\frac{}{}\theta = \alpha</math>
| <math>\frac{\rho\sin(\alpha)}{\alpha}</math>
| <math>\frac{}{}0</math>
| <math>\frac{}{}2\alpha \rho</math>
|
