A man jogs around a regular hexagonal field whose side is 6 m, always staying exactly 3 m away from the nearest edge (on the outside). What total distance does he cover in one complete lap?

Question

Accepted Answer

(36 + 6pi) m. Running 3 m outside a hexagon gives six straight pieces equal to the sides (total 6*6 = 36 m) plus six arcs of radius 3 m whose central angles add up to 360 deg, forming one full circle of circumference 2*pi*3 = 6pi.

A man jogs around a regular hexagonal field whose side is 6 m, always staying exactly 3 m away from the nearest edge (on the outside). What total distance does he cover in one complete lap?

Solution

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