# How to find the focus

## What is centroid

The center of gravity is the geometric center of a laminar object. It can also be described as the average position of all points in a two-dimensional form. For a laminar object of uniform density, when the object is suspended by the center of gravity, the object is balanced. The center of gravity of a convex object is always within the perimeter of the object, while a concave object can have the object outside the perimeter. How to find the center of gravity of an object is explained below.

## Formulas to find the center of gravity

The following formulas give coordinates of the center of gravity of an object.

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

Hence it can be said

If an object is a composition of several geometric objects, the center of gravity of the assembled object can be found more easily on the basis of the centers of gravity of the individual components. If (x i , y i ) are the coordinates of the centroid of the ith component and A i is its area, then the centroid of the composition is given by

If a compound contains a remote area, this area is rated as negative. Even with symmetrical objects, the focus is on the axis of symmetry.

The focal points of common geometric shapes are given below.

Also, if the coordinates of the vertices of a triangle are (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), the coordinates of the center of gravity are given by x C = (x 1 + x 2 + x 3 ) / 3 and y C = (y 1 + y 2 + y 3 ) / 3

## How to find the focus - examples 