Suppose a Kite with coordinates as (0.5,0.5), (1/3,1/3), (0.5, 0) and (1,0)
Centroid abscissa=1/4*(0.5+1/3+0.5+1)=7/12
Consider 2 triangles with coordinates (0.5,0.5), (1/3,1/3), (1,0) and (1/3,1/3), (0.5, 0) and (1,0)
Now, they both have equal areas and both their Centroid Abscissa are 11/18 each.
Thus now Abscissa of COM of the body would be 11/18
Why is it different in different approaches? What point I might be missing?
You are computing the centroid of a triangle or quadrilateral as the arithmetic mean position of their vertices. But only in the case of a triangle (or for some special quadrilaterals) this is the same as the centroid of the area of the figure.
Your reasoning, then, gives you the centroid of the area of the kite, which is in fact the midpoint of the centroids of those two triangles composing it. But this is not the centroid of the kite vertices.
To obtain the centroid of the kite vertices from the triangles, you should consider your triangles but with the vertices they have in common (let's name them $A$ and $B$) having half the mass of the other vertex. In that case the centers of mass of both triangles vertices have abscissa $7/12$.