Because e and f are the midpoint between BC and BD.

Therefore, BE=EC and CF=FD.

So the triangle ABE and AEC have the same base and the same height.

Therefore, the areas of these two triangles are equal, both of which are half the area of triangle ABC.

Similarly, the area of triangle ACF and AFD is equal, which is half of triangle ACD.

So the area of the shaded part is half that of the rectangular ABCD.

That is, the area is 45 square centimeters.