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(b+cd),a\left(b + c\sqrt{d}\right), where a,b,c,da,b,c,d are all positive integers, gcd(b,c)=1,\gcd(b,c) = 1, and dd is square-free, input a+b+c+da + b + c + d as your answer.

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