Question

In ∆ABC, AD is the median to side BC, E is a point on AD such that AE=ED. If ar{∆ ABC} = 144 cm2 find ar{∆DEC}.

Answer 1

in triangle ABC AD is median 
⇒ar[ABD]=ar[ADC]
⇒ar[ADC]=1/2 ar[ABC]              [i]
also CE is median 
⇒ar[DEC]=1/2 ar[ADC]
⇒ar[DEC]=1/2 * 1/2 ar[ABC]            from equation [i]
⇒ar[DEC]=1/4ar[ABC]
               =1/4*144
                = 36 cm ^2