Determine the centroid:

Determine the centroid of the area OBDC as illustrated in Figure

Solution

The trapezium area is divided in two simple areas,

 (i)        A₁ = Rectangle OLDC with centroid (w.r.t. coordinate axes OX and OY) at G₁ (1.5, 3)

 (ii)       Similarly, A₂ = Triangular area DLB = ( 6 × 3)/2= 9 m 2 with its centroid at G₂ (4, 2)

The computation of essential data and the co-ordinates (x¯, y¯) for G are given in Table:

Then,        x¯ =  63/27  = 2.33 m         y¯ =  72 /27 = 2.67 m

Therefore, the co-ordinates of centroid G are x¯ = 2.33 m and y¯ = 2.67 m .