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APMOPS 2010 Question 6

APMOPS · APMOPS 2010

Question 6

$M$ and $N$ are mid-points of the lines $AD$ and $BC$ respectively. Given that the area of $ABCD$ is $2000\text{ cm}^2$, and the area of the shaded region $ANCM=x\text{ cm}^2$, find the value of $x$.

Source note: all vertex labels are missing from the original image. A consistent proposed labeling and an explanation are supplied in the solution.

Question illustration