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Question
D is the mid-point of side BC of ΔABC and E is the mid-point of BD. if O is the mid-point
of AE, prove that ar (ΔBOE) = `1/8` ar (Δ ABC).
Solution
Given that
D is the midpoint of side BC of ΔABC .
E is the midpoint of BD and
O is the midpoint of AE
Since AD and AE are the medians of ΔABC and ABD respectively
∴ ar (Δ ABC) = `1/2` AR (ΔABC) ........... (1)
ar (ΔABE) `1/2` ar (ΔABD) ........... (2)
OB is a median of (ΔABE)
∴ ar (ΔBOE) = `1/2` ar (ΔABE)
From 1, (2) and (3) we have
ar (BOE) =`1/8` ar (ΔABC)
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