The center of gravity of a triangle is its centroid. The centroid of a triangle is the intersection of the three medians.
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The Centroid
Centre of area of a triangle is the centre point for a circumscribed radius which will pass through all 3 vertices of the triangle.
This line is called the bisector (German Halbierende, Dutch bissectrice, Swedish bisektris).In an isosceles triangle the bisector of the side opposite the unequal angle is also perpendicular to that side.In an equilateral triangle all bisectors are perpendicular to the opposite sides.The point in which all bisectors meet in a triangle is called its barycenter (English from Greek meaning "center of gravity") and if the triangle were made of a homogeneous material of infinitesimal height (that is, if it were two-dimensional) it would be indeed its center of gravity.
Center of mass of an equilateral triangle is located at its geometric center (centroid).