Let the vertex be (xr,yr),r=1,2,3, where both xr and yr are integers. Hence, area of triangle =‌‌
1
2
Σx1(y2−y3)=rational number .....(1) Let a be the side of equilateral triangle, then a2=(x1−x2)2+(y1−y2)2=a positive integer. But, the area of an equilateral triangle =
√3
4
a2 ∴ Area =(
√3
4
)a2,which is irrational, since a2 is a positive integer. Thus the two statements (1) and (2) for area are contradictory. Hence, such type of a triangle is not possible.