Detailed explanation of the 18th problem of mathematics in 2009 in Ningde senior high school entrance examination.

The vertical line of Y axis intersects M through A, and the vertical line of X axis intersects N through B. The area of rectangle AMOC is equal to K, and the area of rectangle BDON is also equal to K. The common part of two rectangles is PDOC, so the area of AMDP is equal to BPCN.

The area of ADP is equal to BPC. Obviously, the area of APB is equal to BPC, and the area of ADP is equal to CDP, so the area of each triangle is 3. The area of the rectangular AMOC is equal to 3 times 4, that is, 12.k is equal to 12.

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