We can see from the diagram that the length of the rectangle is 2 lots of the radius of one quarter circle. The width is made up of one radius, therefore the width is half of the length.
This means that the width of the rectangle is 9cm, and the radius of each quarter circle is 9cm.
To find the shaded area, we find the area of the rectangle and subtract from the areas of each circle, which are equal:
A = lw - 1/2(pi x r^2)
A = 9 x 18 - 1/2(81pi)
A = 162 - 81/2 pi
A = 34.8cm (3sf)