In the above diagram, \(ABCD\) is a square and point \(E\) lies on side \(CD\).

Line segment \( AE\) and diagonal \( BD\) intersect at point \( F\), such that \( BF : FD = 4 : 3\).

If the combined area of the 2 blue triangles is \( 100 \text{ cm}^{2} \), find the area of the square in \(\text{cm}^{2} \).

\(\)

**Note:** The figure is not drawn to a scale

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