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SMO 2009 Senior Round 1 Question 6

SMO · SMO 2009 Senior Round 1

Question 6

The area of triangle $ABC$ is $40\text{ cm}^2$. Points $D,E,F$ are on sides $AB,BC,CA$ respectively, as shown. If $AD=3$ cm, $DB=5$ cm, and the area of triangle $ABE$ is equal to the area of quadrilateral $DBEF$, find the area of triangle $AEC$ in $\text{cm}^2$.

Question illustration
  1. $11$
  2. $12$
  3. $13$
  4. $14$
  5. $15$