# Centroid of a Trapezoid

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

between the two bases or in other words lies on the median of trapezoid.  A trapezoid is a 4 sided polygon

that has at least one pair of sides parallel. For a given 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 the formula for Centroid is given by:

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

Example 1:- Find the Centroid of a trapezoid which has sides a = 4 m and b = 2 m and height is h =

3 m.

Solution 1:- For the given question

Base length a=4 m; b=2 m

Height h = 3 m

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

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

X = [(2(4) + (2))/(3 x ((4) + (2)))] x 3

X = [10/18] x 3

X = 1.66 m

The centroid of  trapezoid is 1.66m

Example 2:- Find the Centroid of trapezoid which has sides a = 3 m and b = 5 m and height is h = 2

m.

Solution 2:-   For the given question

Base length a=3 m; b=5 m

Height h = 2 m

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

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

X = [11 /(24)] x 2

X = 0.916 m

The centroid of  trapezoid is 0.916m