A Regular Hexagon = Six Equilateral Triangles
Area of a regular hexagon? Draw lines from the center to each vertex and it splits into six equilateral triangles — related to why bees build hexagons.
Do not write an equation yet. Shake the figure first.
Play the reversal slowly
Now move the same pieces step by step and prove that the pattern you touched was not an accident.
A regular hexagon (side s). How to find its area?
Return to the exact question
Find the area of a regular hexagon (side s) by splitting it from the center into equilateral triangles.
Why this approach works
A regular hexagon has radius equal to its side. Lines from the center make six triangles, each with two sides equal to the radius (= s) and an included angle of 360°/6 = 60° — so each is equilateral. Thus the hexagon is six equilateral triangles: 6 × (√3/4)s² = (3√3/2)s² ≈ 2.598 s². Splitting into known shapes is the core strategy for polygon area.
Proof
Since a regular hexagon has radius equal to its side, the six central triangles are equilateral (two sides s, 60° between). Six times (√3/4)s² gives the hexagon’s area.
Try it yourself
Any regular n-gon splits into n isosceles triangles; as n grows it nears a circle and the area tends to πr² (see #9).
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