Hexagon Area Calculator

Using A = (3 x sqrt(3) / 2) x s^2: A = 2.5981 x 25 = 64.95 square units. This equals the area of 6 equilateral triangles, each with area 10.825 square units.

The apothem is the perpendicular distance from the center of a regular polygon to the midpoint of one side. For a hexagon with side s, the apothem = s x sqrt(3)/2. You can also calculate area as A = (1/2) x perimeter x apothem = (1/2) x 6s x (s x sqrt(3)/2).

If the apothem is a, then the side length s = 2a / sqrt(3). Substitute into the area formula: A = (3 x sqrt(3) / 2) x (2a/sqrt(3))^2 = 2 x sqrt(3) x a^2. For an apothem of 4.33, the area is 2 x 1.7321 x 18.75 = 64.95 square units.

Hexagons tile a flat surface with no gaps while using the least total perimeter (wall material) for a given area. This makes them the most material-efficient shape for covering a plane, which is why bees build hexagonal honeycombs. Basalt columns and snowflakes also form hexagonal patterns due to molecular geometry.

Perimeter = 6 x side length. A hexagon with side 5 has perimeter = 30 units. The circumradius (center to vertex) equals the side length, which is unique to regular hexagons among regular polygons.

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