3. DEFINITION OF CENTROID
•The centroid is the centre point of the object. The
point in which the three medians of the triangle
intersect is known as the centroid of a triangle. It
is also defined as the point of intersection of all
the three medians. The median is a line that joins
the midpoint of a side and the opposite vertex of
the triangle.
4. FORMULA OF CENTROID
• The formula for the centroid of a triangle is used to find
the coordinates of the centroid of a triangle, for which
the coordinates of vertices of the triangle are
known. Centroid = [ x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 ] .
Observe the below figure which shows the vertices of
the triangle in the form of coordinates.
• x1, x2, x3 are the x-coordinates of the vertices of a triangle.
• y1, y2, y3 are the y-coordinates of the vertices of a triangle.
5. EXAMPLE
• Determine the centroid of a triangle whose vertices are (5,3), (6,1) and
(7,8).
• Solution
• Given parameters are,
• (x1, y1) = (5,3)
• (x2, y2) = (6,1)
• (x3, y3) = (7,8)
• The centroid formula is given by
• C = [(x1 + x2 + x3)/ 3, (y1 + y2 + y3)/ 3)
• C = [(5 + 6 + 7) / 3, (3 + 1 + 8) / 3]
• C = (18 / 3, 12 / 3)
• C = (6, 4)
6. PROPERTIES OF CENTROID
•The properties of the centroid are as follows:
•The centroid is the center of the object.
•It is the center of gravity.
•It should always lie inside the object.
•It is the point of concurrency of the medians.
7. CENTER OF MASS
• The center of mass is a position defined relative to an
object or system of objects. It is the average position
of all the parts of the system, weighted according to
their masses.
• For simple rigid objects with uniform density, the
center of mass is located at the centroid
8. CENTER OF GRAVITY
• The center of gravity is the point through which the
force of of gravity is then in exactly the same position as
the center gravity acts on an object or system. In most
mechanics problems the gravitational field is assumed to
be uniform. The center f mass. The terms center of
gravity and center of mass tend to often be used
interchangeably since they are often at the same
location.
9. APPLICATION OF CENTROID
• Support at centroid keeps any structure in
balanced position
• In the calculation of stress and deflectional of
beam ,identification of centroid is very important
• It is also importation designing a concrete wall
