Quadrilateral $ABCD$ satisfies the following conditions: 
- $AB = 8$, 
- $BC = 5$, 
- $CD = 17$, 
- $DA = 10$. 

Let $E$ be the intersection of diagonals $AC$ and $BD$. It is given that the ratio $BE : ED = 1 : 2$. 

Find the area of quadrilateral $ABCD$.

Let's think step by step and output the final answer within \boxed{}.
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