ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AErespectively. IF area of ΔABC is 16 cm2, find the area of ΔDEF.
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 cm2
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 cm2
Area of Δ ADC = 8cm2
For ΔADC , AE is the median .
Area of ΔAED = `1/2 ` (Area of Δ ABC)
`= 1/2 (8)`
= 4 cm2
Area of ΔAED = 4 cm2
Similarly, For ΔAED , DF is the median .
Area of ΔDEF = `1/2 ` (Area of Δ AED)
`= 1/2 (4)`
= 2 cm2
Area of ΔDEF = 2 cm2
Hence we get Area of ΔDEF = 2 cm2
