Question

In $\Delta ABC$, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then ar($\Delta BOE$)=?

• A. $\frac{1}{3}ar\left(\Delta ABC\right)$
• B. $\frac{1}{4}ar\left(\Delta ABC\right)$
• C. $\frac{1}{6}ar\left(\Delta ABC\right)$
• D. $\frac{1}{8}ar\left(\Delta ABC\right)$

Answer 1

The correct option is D $\frac{1}{8}ar\left(\Delta ABC\right)$

In ABC, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE.
Then BE=$\frac{1}{4}$BC OR OE=$\frac{1}{2}$AE
WE know thet area of triangle =$\frac{1}{2}$h.b
Area of triangle ABC=$\frac{1}{2}BC\left(AE\right)$
Area of triangle BOE=$\frac{1}{2}BE\left(OE\right)$
Then area of triangleBOE=$\frac{1}{8}$area of triangleABC