In a ∆ A B C , medians, A D and B E are drawn. If A D = 4 , ∠ D A B = π 6 a n d ∠ A B E = π 3 , then the area of the ∆ A B C is

Step-by-step solution

Since, the centroid G divide the line A D in the ratio 2 : 1 ∴    A G = 8 3   a n d   D G = 4 3 Here, ∆ A B G is a right triangle, since ∠ A G B is π 2 In ∆ A B G ,  tan  ⁡ π 3 = A G B G ⇒     B G = A G  cot  ⁡ π 3 ⇒     B G = 8 3 × 1 3 = 8 3 3 Area of   ∆ A D B = 1 2 × A D × B G = 1 2 × 4 × 8 3 3 = 16 3 3 Since, median divides a