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area computational (2010 HOMC Junior Q9)

Source:

July 18, 2019
geometryarea of a triangleareas

Problem Statement

Let be given a triangle ABCABC and points D,M,ND,M,N belong to BC,AB,ACBC,AB,AC, respectively. Suppose that MDMD is parallel to ACAC and NDND is parallel to ABAB. If S△BMD=9S_{\vartriangle BMD} = 9 cm 2,S△DNC=25^2, S_{\vartriangle DNC} = 25 cm2^2, compute S△AMNS_{\vartriangle AMN}?
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