triangle AEB ~ triangle DEC

Therefore,  AE/ED = CD/AB

That is, x/(4-x) = 9/3

On simlifying, we get x = AE = 1 and DE = 3

Area of triangle ADC = 1/2 × CD × AD = 1/2 × 9 × 4 = 18

Area of triangle EDC = 1/2 × 9 × 3 = 13.5

Therefore, Area of triangle AEC = Area of triangle ADC – Area of triangle EDC

                                                          = 18 – 13.5

                                                          = 4.5

That is Option D is the correct answer.