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Question
Medians of ΔABC intersect at G. If ar (ΔABC) = 27 cm2, then ar (ΔBGC) =
Options
6 cm2
9 cm2
12 cm2
18 cm2
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Solution
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
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