Problem 1343 (difficulty: 4/10)

The vertices of a triangle are \(\displaystyle A=(a,0)\), \(\displaystyle B=(b,0)\) and \(\displaystyle C=(0,m)\). For \(\displaystyle (x,y)\in[0,1]^2\) let

\(\displaystyle f(x,y) = (1-x)(1-y)\cdot A + x(1-y)\cdot B + y\cdot C. \)

Use this map and the theorem on measure transformation to determine the area of the triangle.

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