Question

In triangle ABC, AD, BE and CF are medians and G is the centroid of the triangle. If the area of the triangle DGC is 20 cm², then the area of triangle AGF + the area of triangle BGF is equal to:
1. 40 cm2
2. 30 cm2
3. 20 cm2
4. 25 cm2

Answer 1

Correct Answer - Option 1 : 40 cm2

Given :

In triangle ABC, AD, BE and CF are medians and G is the centroid of the triangle and the area of the triangle DGC is 20 cm².

Concept used :

All medians of a triangle divides a triangle in 6 triangles of equal area. 

Calculations :

Area of triangles AGF, AGE, DGB, DGC, EGC and FGB are equal. 

∆ DGC = 20 cm²

So, 

∆ AGF = ∆ BGF = 20 cm²

∆ AGF + ∆ BGF = 20 + 20 

⇒ 40 cm²

∴ Option 1 will be the correct answer.