The following diagrams depict a list of centroid

Centroid

In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" of all points of X...

s. A centroid of an object in -dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

al space is the intersection of all hyperplane

Hyperplane

A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.A hyperplane of an n-dimensional space is a flat subset with dimension n − 1...

s that divide into two parts of equal moment

Moment (physics)

In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...

 about the hyperplane. Informally, it is the "average

Average

In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

" of all points of . For an object of uniform composition (mass, density, etc.) the centroid of a body is also its centre of mass.

Shape	Figure			Area
Right-triangular Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....  area
Quarter-circular area
Semicircular Semicircle In mathematics , a semicircle is a two-dimensional geometric shape that forms half of a circle. Being half of a circle's 360°, the arc of a semicircle always measures 180° or a half turn...  area
Quarter-elliptical area
Semielliptical area
Semiparabolic area	The area between the curve and the axis, from to
Parabolic Parabola In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...  area	The area between the curve and the line
Parabolic spandrel	The area between the curve and the axis, from to
General spandrel	The area between the curve and the axis, from to
Circular sector Circular sector A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r the radius of the circle, and L is the arc length of the...	The area between the curve (in polar coordinates) and the pole, from to
Circular segment Circular segment In geometry, a circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center...
Quarter-circular arc	The points on the circle and in the first quadrant
Semicircular arc	The points on the circle and above the axis
Arc of circle Circle A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....	The points on the curve (in polar coordinates) , from to

External links

• 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