Areas Inside a Rectangle

Geometry Level 4

ABCDABCD is a rectangle with point EE on line segment ABAB and point FF on line segment BCBC such that [ADE]=7[ADE] = 7, [BEF]=11[BEF] = 11 and [DCF]=9[DCF] = 9. Then [DEF]=ab[DEF] = a\sqrt{b}, where aa and bb are integers and bb is not a multiple of the square of any prime. What is the value of a+ba + b?

Details and assumptions

[PQRS][PQRS] denotes the area of figure PQRSPQRS.

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