3-4-5 Square

Geometry Level 3

The diagram above illustrates a square divided into four different-colored triangles, three of them with numbers given as their respective areas.

What is the area of the whole square?

If your result can be expressed in the form \[a\left(b + c\sqrt{d}\right),\] where \(a,b,c,d\) are all positive integers, \(\gcd(b,c) = 1,\) and \(d\) is square-free, input \(a + b + c + d\) as your answer.

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