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Problem of the Week
Problem D
They’re Blue

In rectangle \(ABCD\), the length of side \(AB\) is \(7\) m and the length of side \(BC\) is \(5\) m. Four points, \(W\), \(X\), \(Y\), and \(Z\), lie on diagonal \(BD\), dividing it into five equal segments. Triangles \(AWX\), \(AYZ\), \(CWX\), and \(CYZ\) are then painted blue, as shown.

Along diagonal BD, point W is closest to
vertex D and the points W, X, Y, and Z are placed in order, with Z
closest to B.

Determine the area of the painted region.