Three circles are placed on a plane in such a way that each circle just touches the other two each having a radius of 10 cm. Area of the region enclosed by them.

Answer 1

the circle centers form an equilateral triangle with side 10.
area of triangle is thus √3/4 10^2 = 25√3

each side of the triangle subtends an angle of π/3, and the segment formed has area 1/2 *25*(π/3-√3/2) = 25/12 (2π-3√3).

Subtract the area of the 3 segments from the triangle, leaving

25√3 - 25/4 (2π-3√3) =~ 36.5

you can massage that if you want.

Answer 2

oops - I used a diameter of 10 cm. Adjust accordingly.