# Parallelogram with extended side lengths

Geometry Level pending

$$ABCD$$ is a parallelogram. Let $$C'$$ be a point on $$AC$$ extended such that the length of $$AC'= 1.2 AC$$. Let $$D'$$ be on the segment $$BD$$ such that the length of $$BD' = 0.9 BD$$. The ratio of the area of the quadrilateral $$ABC'D'$$ to the area of the parallelogram $$ABCD$$ can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

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