MathDB

A snail begins a journey starting at the origin of a coordinate plane. The snail moves along line segments of length

\sqrt{10}

and in any direction such that the horizontal and vertical displacements are both integers. As the snail moves, it leaves a trail tracing out its entire journey. After a while, this trail can form various polygons. What is the smallest possible area of a polygon that could be created by the snail's trail?

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