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area wanted, triangle inscribed in square (2016 Auckland MO J3)

Source:

December 30, 2020
geometryareassquare

Problem Statement

Triangle XYZXYZ is inside square KLMNKLMN shown below so that its vertices each lie on three different sides of the square. It is known that: \bullet The area of square KLMNKLMN is 11. \bullet The vertices of the triangle divide three sides of the square up into these ratios: KX:XL=3:2KX : XL = 3 : 2 KY:YN=4:1KY : YN = 4 : 1 NZ:ZM=2:3NZ : ZM = 2 : 3 What is the area of the triangle XYZXYZ? (Note that the sketch is not drawn to scale). https://cdn.artofproblemsolving.com/attachments/8/0/38e76709373ba02346515f9949ce4507ed4f8f.png