# How to Find the Centroid

## What is Centroid

The centroid is the geometric center of a laminar object. It can also be described as the average position of all the points in a two-dimensional shape. For a laminar object with uniform density, when suspended through the centroid, object obtains equilibrium. The centroid of a convex object always lies within the perimeter of the object, while for a concave object the object may lies outside the perimeter. How to find the centroid of an object is explained below.

## Formulae to find the Centroid

The following formulae give coordinates of the centroid of an object.

Where f is the characteristic function of the geometric object,(A function that describes the shape of the object,product f(x) dx usually provides the incremental area of the object.

Therefore, it can be stated,

If an object is a composition of several geometric objects, then it is easier to find the centroid of the composite object using the centroids of the individual components. If (xi,yi ) are the coordinates of the centroid of ith component and Ai is its area, then the centroid of the composite is given by,

If a composite includes an area removed, its area is taken as negative. Also, if the objects are symmetric, then the centroid lies on the axis of symmetry.

The position centroids of common geometric shapes are given below.

Additionally, if the coordinates of the vertices of a triangle are(x1,y1),(x2, y2) and ( x3,y3) the coordinates of the centroid are given by xC=(x1+x2+x3)/3 and yC=(y1+y2+y3)/3

## Related pages

stratified tissue definitionwhat is difference between vegan and vegetarianmeaning didacticassonance sentence examplesdistinguish between a compound and a mixturewhat is coagulation and flocculationaddition condensation polymerizationexamples of moneransenglish mastiff bullmastiffbf skinner operant conditioning theory pptwhat is guar gum and xanthan gumwhat is celpipencephalitis or meningitiswhat is the difference between an anion and a cationalfa heliksdaytime semi formal attirecompare vaporization and evaporationdifference between syllable and morphemedifference between a nutritionist and dietitiandefinition of vowels and consonantsmalamutes vs huskywhat are consonants soundssn1 mechanism stepsdiploid wikipediamonozygotic and dizygotic twinswhat is the difference between hotel and innpolymer vs monomerthe ant and the lion storytypes of consonants soundsnemesis meandistinguish between sexual and asexual reproductionprejudice and racism differencewhat is the difference between informative and explanatory writinglacquer nail polish vs nail polishrecession versus depressionexamples of irony and sarcasmwhat is the difference between watts and vawhat is the difference between messenger rna and transfer rnapiaget adaptation theorystructural formula of maltoseexample of nonpolar moleculesintermolecular and intramolecularis sleep a nounfunction of carrier proteinswriting in iambic pentameterwhat is polyploidysn1 vs sn2 reaction mechanismdefine man made disastersdifference between meiosis and mitosisreversal satire definitionthe difference between envy and jealousydifference between herbivore carnivore and omnivorewhat is the difference between dewpoint and relative humiditymarxist literaturedifference between hemoglobin and myoglobinexamples of diminishing marginal returnsshark fish or mammalwhat is an example of a nonpolar moleculedefinition of melting point and boiling pointadjunct in english grammarguar gum or xanthan gumdefinition of regular hexagonbiannual biennialcarbon content of wrought irontardive dystonia symptomsmsc degree stands forjuxtaposition examples literaturephonetics vs phonologyprinciple of conservation of linear momentumwhat is the difference between custard and ice creambasil or tulsicarbon steel vs mild steelwhat is the meaning of leukocytosismono polyunsaturated fats