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UKMT Senior Mathematical Challenge, 2022

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The shape shown is made by removing four equilateral triangles with side-length $1$ from a regular octagon with side-length $1$ . What is the area of the shape?

(A) $2-2\sqrt{2}+\sqrt{3}$ (B) $2+2\sqrt{2}-\sqrt{3}$ (C) $2+2\sqrt{2}+\sqrt{3}$ (D) $3-2\sqrt{2}-\sqrt{3}$ (E) $2-2\sqrt{2}-\sqrt{3}$

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