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.

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.

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

To find the area of the region enclosed by the three circles, we need to determine the shape of the enclosed region.

When three circles touch each other externally, they form an equilateral triangle. In this case, each circle is tangent to the other two, and the centers of the circles form an equilateral triangle.

Given that each circle has a radius of 10 cm, the sides of the equilateral triangle formed by the centers of the circles will also have a length of 10 cm.

To find the area of the equilateral triangle, we can use the formula:

Area = (√3 / 4) * s^2

where s is the length of a side of the triangle.

In this case, s = 10 cm, so the formula becomes:

Area = (√3 / 4) * 10^2

Area = (√3 / 4) * 100

Simplifying further:

Area = (1.732 / 4) * 100

Area = 43.3 cm^2