# Octagram and octagon

Geometry Level 3

The diagram below shows a regular octagram and a regular octagon.

Given that $$AB = \sqrt{2}-1 \text{ cm}$$ and the area of $$\triangle EMT$$, $$[EMT] = \dfrac{ a \sqrt{b} - c }{4} \text{ cm}^2$$, where $$a$$ , $$b$$ and $$c$$ are positive integers and $$b$$ is square-free , find $$a+b+c$$.

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