Question

In a triangle ABC, E is the mid-point of median
AD. Then
(1) ar( BED) = 1/4 ar(ABC)
(2) ar( BED) = ar(ABC)
(3) ar(BED) = 1/2 ar(ABC)
(4) ar(BED) = 2 ar(ABC)​

Answer 1

$\color{lime}\tt \huge \underline{ \color{red}Solution}$

Consider ∆ABC

Area of (∆ACD) = Area of (∆ABD)

= $\frac{1}{2}$ area of (∆ABC)

as D is median

Considering ∆ADB, E is a median

area of (∆AEB) = area of (∆DBE) = $\frac{1}{2}$ area of (∆ADB)

area of (∆BED) = $\frac{1}{2}$($\frac{1}{2}$area of (∆ABC)

area of (∆BED = $\frac{1}{4}$ × area of (∆ABC)