(1) According to the known conditions: ① When the umbrella is tightened, point P coincides with point A; ②PM=PN=CM=CN=6 decimeters. It can be seen that when the umbrella is tightened, CP=CA=CN+PN= 12 decimeter and BC=2 decimeter, so AB=CA-BC= 12-2= 10 decimeter.

Then 0≤X≤ 10 (that is, 0≤AP≤AB).

(2) If the angle CPN = 60 and CN=PN, then △CPN is an equilateral triangle, then CP=6 decimeters, and X=AP= 12-CP=6 decimeters.

(3) The shadow area of an umbrella under direct sunlight is actually the area of a circle with EF as its diameter. Connect EF and CA at point d, right triangle CFD, according to pythagorean theorem: DF? =CF？ -CD？ And CD = ca-x =12-X.

Shadow area under umbrella Y=π×DF? =π×(CF？ -CD？ )=π×{ 18? -( 12-X)？ }=

Work out the result, do the calculation, and it's done. )