Question

prove that the median of a triangle divides it into two triangles of equal areas. hence find arABD if ar(?ABC) =30 cm2 where AD is the median.

Answer 1

From the figure attached with this answer shows that, ΔABC be the triangle. AD be the median of side AB. The point bisect the side AB. So AD = BD. The  median AD divide the ABC into two triangles, ΔADC and ΔBDC. the height of these two triangle is same denoted by 'h'.

area of ΔADC= 1/2(AD x h) =1/2(1/2(AB) x h) =1/2(BD x h) area of BDC

So the median divides the triangle into 2 triangle with equal area.

In the question ar (ABC) = 30 cm^2

Therefore ar(ADC) =1/2(ar(ABC))=1/2 x 30 =a5 cm^2