Question

Medians of ΔABC intersect at G. If ar (ΔABC) = 27 cm², then ar (ΔBGC) =

Options

• 6 cm²

•  9 cm²

• 12 cm²

•  18 cm²

Answer 1

Given: (1) Median of ΔABC meet at G.

(2) Area of ΔABC = 27 cm²

To find: Area of ΔBCG.

We know that the medians of the triangle divides each other in the ratio of 2:1

Hence,

ar (ΔBED) = `1/2 xx BC xx GD`

ar (ΔBED) =`1/2 xx BC xx 1/3 (AD)`

ar (ΔBED) =`1/3(1/2xx AD xx BC)`

ar (ΔBED) =`1/3 (Δ ABC)`

ar (ΔBED) = = `1/3(27)`

ar (ΔBED) == 9 cm²