Centroid of a Trapezoid

Centroid of a Trapezoid 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