The centroid of a triangle with vertices (2a,b),(-b,a) and (b,3a) is (4,11). The area of the triangle is ___ square units.

Coordinates of centroid of the triangle = $$\ \left(\dfrac{x_1+x_2+x_3\ }{3},\ \dfrac{\ y_1+y_2+y_3}{3}\right)$$

$$\ \dfrac{\ 2a}{3}=4$$

a = 6

$$\ \dfrac{\ b+4a}{3}=11$$

$$\ \ b=9$$

Thus, the coordinates of the triangle are (12,9), (-9,6) and (9,18).

Using the determinant formula to calculate the area of the triangle, we get

Area = $$\ \ \ \dfrac{\ 1}{2}\left|12\left(6-18\right)-9\left(18-9\right)+9\left(9-6\right)\right|$$

= $$\ \ \ \dfrac{\ 1}{2}\left|-144-81+27\right|$$

= $$99$$ square units