Calculate regular hexagon area, perimeter, apothem, long diagonal, short diagonal, and circumradius with step-by-step steps.
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A regular hexagon is a six-sided polygon with six equal sides and six equal interior angles of 120°. It is composed of six congruent equilateral triangles meeting at the center.
A = \frac{3\sqrt{3}}{2}s^2 \approx 2.59808s^2, \quad P = 6s, \quad d_{\text{long}} = 2s, \quad d_{\text{short}} = s\sqrt{3}Because a regular hexagon consists of 6 equilateral triangles of area (√3/4)s², total area is 6 × (√3/4)s² = (3√3/2)s².
Scenario: Find area and diagonals for a regular hexagon with side s = 8 cm
Perimeter: P = 6 × 8 = 48 cm
Area: A = (3√3 / 2) × 8² = (3√3 / 2) × 64 = 96√3 ≈ 166.2769 cm²
Long diagonal: d_long = 2 × 8 = 16 cm
Short diagonal: d_short = 8√3 ≈ 13.8564 cm
Each interior angle is 120°. Three hexagons meet at a vertex: 120° × 3 = 360°, leaving no gaps and no overlap.
The long diagonal connects opposite vertices through the center (d = 2s). The short diagonal connects vertices separated by one corner (d = s√3).
The sum is (6 - 2) × 180° = 720°. Divided by 6, each angle is 120°.
First divide perimeter by 6 to find side s, then apply A = (3√3/2)s².
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