If the area of the triangle BGC is 28 square units and the centroid of the triangle is G, then find the area of the triangle ABC.

To find the area of triangle ABC, we can use the property of the centroid in relation to the areas of triangles formed with it.

The centroid (G) of a triangle divides it into three smaller triangles (BGC, CAG, and ABG), and the area of each of these smaller triangles is equal to one-third of the area of the whole triangle.

Given that the area of triangle BGC is 28 square units, we can conclude that the total area of triangle ABC is three times the area of triangle BGC.

So, we calculate it as follows:

Area of triangle ABC = 3 × Area of triangle BGC = 3 × 28 = 84 square units.

Therefore, the area of triangle ABC is 84 square units.