Ritika,
There are 2 parts to this problems.
First - the area of the hexagon. SInce the perimeter is 36, each side is 6 and the hexagon is a combination of 6 equilateral triangles.
Since the area of 1 equilateral triangle is root 3/4 * a^2
The total area of the hexagon equals the area of 6 equilateral triangles - ie root 3/4 * 6^2 = 54root3
Area of circles - If the circles are tangent to each other then the radii of each circle is equal ie: 3
Area of 1 circle - pi r^2 ie 9*pi
Area of 6 circles - 54 pi. But the area of circle within the hexagon is only one third the area (because the angle subtended by one angle of a hexagon is 120 degrees)
Therefore the area of 6 circles within the hexagon is 18pi.
if the inner circle is also tangent, then the whole are is 9 pi.
Shaded are equals Area of hexagon - Area of circles ie; 54root 3 - 27pi
