# Centroid of Trapezoid

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Centroid of trapezoid is a useful tool to find the centre of the trapezoid. Geometrically the Centroid of a

trapezoid is between the two bases or in other words lies on the median of trapezoid.  A trapezoid is a

quadrilateral ( a 4 sided polygon )  that has ( at least one pair ) 2 sides parallel. The formula for the centroid

of trapezoid that has parallel side a and b where the b is the base and height is h and Centroid is above b at

a distance of x is given by:

X = [(2a + b) / (3 x (a + b))] x h

Example 1:- Find the Centroid of trapezoid which has sides a = 5 m and b = 7 m and height is h = 9

m.

Solution 1:- For the given question

Base length a=5 m; b=7 m

Height h=9 m

Centre of the trapezoid  X = [(2a + b)/(3 x (a + b))] x h

X = [(2(5) + (7))/(3 x ((5) + (7)))] x 9

X = [17/(36)] x 9

X = 4.25 m

The centroid of  trapezoid is 4.25cm

Example 2:- Find the Centroid of trapezoid which has sides a = 5 m and b = 7 m and height is h = 9

m.

Solution 2:- For the given question

Base length a=6 m; b=8 m

Height h = 5 m

Centre of the trapezoid X = [(2a + b)/(3 x (a + b))] x h

X = [(2(6) + (8)) /(3 x ((6) + (8)))] x 5

X = [20 /(42)] x 5

X = 2.38 m

The centroid of  trapezoid is 2.38m