ABC is a triangle in which D is the mid-point of BC. E and F are mid-

1.	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 ΔABC is 16 cm2, find the area of ΔDEF.
Answer» Given that, D, E, F are the mid-points of BC, DC, AE respectively Let, AD is median of triangle ABC Area (ΔADC) = \(\frac{1}{2}\)Area (ΔABC) = \(\frac{1}{2}\) x 16 = 8 cm² Now, AE is a median of ΔADC Area (ΔAED) = \(\frac{1}{2}\)Area (ΔADC) = \(\frac{1}{2}\) x 8 = 4 cm² Again, DE is the median of ΔAED Area (ΔDEF) = \(\frac{1}{2}\)Area (ΔAED) = \(\frac{1}{2}\) x 4 = 2 cm²

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 ΔABC is 16 cm2, find the area of ΔDEF.

Answer»

Given that,

D, E, F are the mid-points of BC, DC, AE respectively

Let,

AD is median of triangle ABC

Area (ΔADC) = \(\frac{1}{2}\)Area (ΔABC)

= \(\frac{1}{2}\) x 16

= 8 cm²

Now,

AE is a median of ΔADC

Area (ΔAED) = \(\frac{1}{2}\)Area (ΔADC)

= \(\frac{1}{2}\) x 8

= 4 cm²

Again,

DE is the median of ΔAED

Area (ΔDEF) = \(\frac{1}{2}\)Area (ΔAED)

= \(\frac{1}{2}\) x 4

= 2 cm²