A point O is taken inside an equilateral ΔABC. If OL 
BC, OM 
AC and ON 
AB such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of 
ABC.
Let each side of 
be a cm
So, area (
) = Area (
) + Area (
) + Area (
)
On taking “a” as common, we get,
= 15a cm2 (i)
As, triangle ABC is an equilateral triangle and we know that:
Area of equilateral triangle = 
cm2 (ii)
Now, from (i) and (ii) we get:
15a = 
15 × 4 = 
60 = 
a = 
a = 20√3 cm
Now, putting the value of a in (i), we get
Area (
) = 15 × 20√3
= 300√3 cm2
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