5 AABC is an equilateral triangle with side 6 cm. D, E, and Fare the mid-points of the sides AB, BC, and AC respectively. (a) Prove that AADF = ADBE = AEFD= AFEC (b) Find the area of ADEF. A B E C
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0
Answer:
The correct option is C 9 cm
Given that,
The side of the equilateral triangle = 6 cm,
AB = BC = AC = 6 cm.
In △ABC,
F and E are the mid-points of AB and AC.
By mid point theorem,
∴
E
F
=
1
2
B
C
=
1
2
×
6
=
3
c
m
Similarly ED = DF = 3 cm
∴
Perimeter of △DEF = 3
×
3 = 9 cm
Hence, the perimeter of the △DEF is 9 cm
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