# 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). - Mathematics

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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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 24 | Page 47