The bird’s-eye tipi

A regular hexagon with triangles to an internal point. What fraction is shaded?

Scroll down for a solution to this problem.


The shaded fraction is 1/2.

Visual solution by David Andriana.

This elegant solution to basically the same puzzle by Mustafa K. Ince expands the regular hexagon to an equilateral triangle of 3/2 the area. Using the fact that each triangle is tripled in area, because the base is three times as large and the height is the same, the required fraction follows.


C’est le toit d’1 tipi
L’habitation des indiens
Une tente de forme conique
Une hutte à toit pointue
Une niche qui abrite la famille et le feu
Cette forme est un tripode
Connectée au Grand Mystère
Ainsi qu’aux étoiles
Pour élever l’âme et faire la prière.


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