# In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) *= *1/4 ar(ABC).

**Solution:**

We know that the median of a triangle divides it into two triangles of equal areas. AD is a median for triangle ABC and BE is the median of ΔABD.

Since AD is the median of ΔABC, so it will divide ΔABC into two equal triangles.

∴ ar (ΔABD) = ar (ΔADC)

Also, ar (ΔABD) = 1/2 ar(ABC) .....(i)

Now, In ΔABD, BE is the median,

Therefore, BE will divide ΔABD into two equal triangles

ar (ΔBED) = ar (ΔBAE) and ar (ΔBED) = 1/2 ar(ΔABD)

ar (ΔBED) = 1/2 × [1/2 ar(ABC)] (Using equation (i))

∴ ar (ΔBED) = 1/4 ar(ΔABC)

**Video Solution:**

## In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) *= *1/4 ar(ABC).

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.3 Question 2:

**Summary:**

If E is the mid-point of the median AD of triangle ΔABC, then Area of (ΔBED) = 1/4 Area of (ΔABC).