Look a little closer.

Six triangles hiding in one shape. These connections help explain why the figure behaves as it does, beyond simply entering numbers into a formula.

01 / A useful relationship

Three regular hexagons meet at a vertex to tile the plane.

Every interior angle is 120 degrees. The distance across opposite vertices is 2a, while the distance across opposite parallel sides is √3a. Its apothem is √3a/2.

02 / A different perspective

The area is six times the area of an equilateral triangle of the same side.

A regular hexagon has six equal sides and six equal angles. Its centre divides it into six equilateral triangles. This special structure makes its circumradius exactly equal to its side length.

03 / A connection to explore

Across-flats and across-corners dimensions are not interchangeable.

The side and radius tools support tile layouts and idealised hexagonal drawings. Real nuts, honeycomb walls and material patterns have thickness, clearance and manufacturing conventions beyond a pure polygon.

Try the idea with numbers

Open the from a side calculator, note its outputs, then multiply each length input by two. Area should increase by four and every reported length should double, when every relevant length is doubled. Angle inputs and dimensionless ratios remain unchanged. This scaling experiment checks the structure of the formula rather than the precision of any real measurement.

Further reading: Regular hexagon at Wolfram MathWorld.