In the given figure, D is the mid-point of BC and E is the mid-point of AD. Prove that :

ar (ΔABE) = $\dfrac{1}{4}$ ar (ΔABC).

Median AD divides triangle ABC into two triangles ABD and ACD of equal area.

ar (△ABD) = $\dfrac{1}{2}$ ar (△ABC) …..(1)

Since E is the mid-point of AD, BE is the median of ΔABD.

ar (△ABE) = $\dfrac{1}{2}$ ar (△ABD) …..(2)

Substituting value from equation 1 in equation 2, we get :

ar (△ABE) = $\dfrac{1}{2} \times \Big(\dfrac{1}{2} \text{ar (△ABC)}\Big)$

ar (△ABE) = $\dfrac{1}{4}$ ar (△ABC).

Hence, proved that ar (△ABE) = $\dfrac{1}{4}$ ar (△ABC).