Lost inside a convex hull!

Geometry Level 4

An ant is trapped inside a convex hull shape with vertices \(v_1, v_2, \ldots, v_k \) and an area of 1.

The ant wants to walk out of this shape by following a predetermined path, which guarantees that the ant will be able to eventually escape. What is the minimum length of such a path?

Give your answer to 3 decimal places.

Note: If the path was along a straight line, then there is no minimum length that would guarantee the ant will be able to eventually escape.

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