*ABC* is a triangle in which *D* is the mid-point of *BC*. *E *and *F* are mid-points of *DC* and *AE*respectively. IF area of Δ*ABC* is 16 cm^{2}, find the area of Δ*DEF*.

#### Solution

**Given:** Here from the given question we get

(1) ABC is a triangle

(2) D is the midpoint of BC

(3) E is the midpoint of CD

(4) F is the midpoint of A

Area of ΔABC = 16 cm^{2}

**To find :** Area of ΔDEF

**Calculation: **We know that ,

**The median divides a triangle in two triangles of equal area. **

For ΔABC, AD is the median

Area of Δ ADC = `1/2 `(Area of ΔABC )

`=1/2 (16)`

= 8 cm^{2}

Area of Δ ADC = 8cm^{2}

For ΔADC , AE is the median .

Area of ΔAED = `1/2 ` (Area of Δ ABC)

`= 1/2 (8)`

= 4 cm^{2}

Area of ΔAED = 4 cm^{2}

Similarly, For ΔAED , DF is the median .

Area of ΔDEF = `1/2 ` (Area of Δ AED)

`= 1/2 (4)`

= 2 cm^{2}

Area of ΔDEF = 2 cm^{2}

Hence we get Area of ΔDEF = **2 cm ^{2}**