Question

Show that the median of a triangle divides the triangle into 2 equal triangle area

Answer 1

Consider triangle ABC with AD the median. So,
In triangle ABC,
ar(ABC)=1/2*b*h .....(1)
ar(ABD)=1/2*(1/2*b)*h(Median divides base into two halves)
             =1/4*b*h
So, ar(ABD)/ar(ABC)=(1/4*b*h)/(1/2*b*h)
                                 =(1/4)/(1/2)
                                 =(1/4)*2
                                 =1/2
therefore ar(ABD)=(1/2)*ar(ABC)
Similarly ar(ADC)=(1/2)*ar(ABC)

Hence median divides a triangle into two triangles of equal area.