Given:
Three equal circles of radius
4cm touch each other
Formula Used:
Area of circle
=πr2 Area of equilateral triangle
=√3a2∕4 Where,
r= radius of circle and
a= side of an equilateral triangle
Calculation:
According to the question
We can draw figure like this
Now, From figure, we can say that
AB=BC=CA=8cm So,
△ABC is an equilateral triangle
And we know that angles of equilateral triangle is
60∘ Now, Area of shaded region
= Area of
△ABC - Area of sectors formed in three circles
⇒ Area of shaded region
=(8)2−3×π(4)2 ⇒16√3−8π square
cm ∴ The area of shaded region is
16√3−8π square
cm.