Question

triangle ABC is an equilateral triangle D1, E1, E1 are midpoint of AB,BC,CA, respectively. similarly D2,E2,F2are midpoint of E1,F1,and D1,E1 respectively. if length of AB=BC=CA=2⁴√3cm. then find the area of D2 E2 F2​

Answer 1

Solution

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Let ABC be the triangle and D, E and F be the mid-point of BC, CA and AB respectively. We have to show triangle formed DEF is an equilateral triangle. We know the line segment joining the mid-points of two sides of a triangle is half of the third side.

Therefore DE=

2

1

AB,EF=

2

1

BC and FD=

2

1

AC

Now, ΔABC is an equilateral triangle

⇒AB=BC=CA

⇒

2

1

AB=

2

1

BC=

2

1

CA

⇒DE=EF=FD

∴ΔDEF is an equilateral triangle.