Determine the centroid of the area:
Determine the centroid of the area OBDC
Solution
The trapezium area is divided in two simple areas,
(i) A_{1} = Rectangle OLDC with centroid (w.r.t. coordinate axes OX and OY) at G_{1} (1.5, 3)
(ii) Similarly, A_{2} = Triangular area DLB = ( 6 × 3)/2= 9 m 2 with its centroid at G_{2} (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.