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