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Points $A(0,0), B(6,0), C(6,10)$ and $D(0,10)$ are vertices of rectangle $A B C D$, and $E$ is on segment $C D$ at $(2,10)$. What is the ratio of the area of triangle $A D E$ to the area of quadrilateral $A B C E$ ? Express your answer as a common fraction.
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The area of triangle $A D E$ is $\frac{1}{2}(10)(2)=10$ square units, and the area of rectangle $A B C D$ is $(6)(10)=60$ square units. Subtracting, we find that the area of $A B C E$ is 50 square units. Therefore, the ratio of the area of triangle $A D E$ to the area of quadrilateral $A B C E$ is $10 / 50=\frac{1}{5}$.

Final Answer: The final answer is $\frac{1}{5}$
by Diamond (66,887 points)

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