Centroid of Trapezoid

Centroid of Trapezoid 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