# Area of Morley's Triangle

**Geometry**Level 5

*First Morley Triangles*. Observe the following image:

The triangle shown above is a 45-45-90 triangle with a hypotenuse of length 4. If the area of the First Morley Triangle depicted in this image can be written as \(a\sqrt{b}-c\), where \(a\), \(b\), and \(c\) are positive integers and \(b\) is square-free, what is \(a+b+c\)?