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نام	نگاره	${\bar {x}}$	${\bar {y}}$	مساحت
مثلث راست‌گوشه		${\frac {-b}{3}}$	${\frac {h}{3}}$	${\frac {bh}{2}}$
ربع دایره		${\frac {4r}{3\pi }}$	${\frac {4r}{3\pi }}$	${\frac {\pi r^{2}}{4}}$
نیم‌دایره	| align="center"|$\,\!0$	0	${\frac {4r}{3\pi }}$
ربع بیضی	| align="center"|${\frac {4a}{3\pi }}$	${\frac {4b}{3\pi }}$	${\frac {\pi ab}{4}}$
نیم‌بیضی		$\,\!0$	${\frac {4b}{3\pi }}$	${\frac {\pi ab}{2}}$
نیمه سهمی گون	The area between the curve $y={\frac {h}{b^{2}}}x^{2}$ and the $\,\!y$ axis, from $\,\!x=0$ to $\,\!x=b$	${\frac {3b}{8}}$	${\frac {3h}{5}}$	${\frac {2bh}{3}}$
سهمی	The area between the curve $\,\!y={\frac {h}{b^{2}}}x^{2}$ and the line $\,\!y=h$	$\,\!0$	${\frac {3h}{5}}$	${\frac {4bh}{3}}$
Parabolic spandrel	The area between the curve $\,\!y={\frac {h}{b^{2}}}x^{2}$ and the $\,\!x$ axis, from $\,\!x=0$ to $\,\!x=b$	${\frac {3b}{4}}$	${\frac {3h}{10}}$	${\frac {bh}{3}}$
General spandrel	The area between the curve $y={\frac {h}{b^{n}}}x^{n}$ and the $\,\!x$ axis, from $\,\!x=0$ to $\,\!x=b$	${\frac {n+1}{n+2}}b$	${\frac {n+1}{4n+2}}h$	${\frac {bh}{n+1}}$
قاچ دایره	The area between the curve (in polar coordinates) $\,\!r=\rho$ and the pole, from $\,\!\theta =-\alpha$ to $\,\!\theta =\alpha$	${\frac {2\rho \sin(\alpha )}{3\alpha }}$	$\,\!0$	$\,\!\alpha \rho ^{2}$
قطعه دایره		$\,\!0$	${\frac {4R\sin ^{3}{\frac {\theta }{2}}}{3(\theta -\sin {\theta })}}$	${\frac {R^{2}}{2}}(\theta -sin{\theta })$
Quarter-circular arc	The points on the circle $\,\!x^{2}+y^{2}=r^{2}$ and in the first quadrant	${\frac {2r}{\pi }}$	${\frac {2r}{\pi }}$	${\frac {\pi r}{2}}$
کمان نیم دایره	The points on the circle $\,\!x^{2}+y^{2}=r^{2}$ and above the $\,\!x$ axis	$\,\!0$	${\frac {4r}{\pi 3}}$	$\,\!\pi r$
کمان دایره	The points on the curve (in polar coordinates) $\,\!r=\rho$ØŒ from $\,\!\theta =-\alpha$ to $\,\!\theta =\alpha$	${\frac {\rho \sin(\alpha )}{\alpha }}$	$\,\!0$	$\,\!2\alpha \rho$

منابع

ویکی‌پدیای انگلیسی

پیوند به بیرون

• http://www.engineering.com/Library/ArticlesPage/tabid/85/articleType/ArticleView/articleId/109/Centroids-of-Common-Shapes.aspx
• http://www.efunda.com/math/areas/IndexArea.cfm