Question

In a triangle ABC,E is the mid point of median AD show that are(triangle BED)=1/4 are triangle ABC

Answer 1

We know that ABC is a triangle and AD is the median. Now, we know that a median divides a triangle into two triangles of equal areas.

Therefore, we get that AR(ABD) = AR(ADC)

Now as we are given E is the midpt. of median AD. Therefore, BE becomes a median as well.
(A median divides a triangle into two triangles of equal areas)

Therefore, AR(ABE)=AR(BED)
Now,AR(BED)=1/2AR(ABD)

AR(ABD)=1/2AR(ABC)
Therefore, AR(BED)=1/4AR(ABC)

Tip : Draw the figure of the triangle. This will help you to understand the question better