Calculate area, perimeter, interior angle, exterior angle, and apothem for any regular polygon
Minimum 3 sides (triangle), maximum 100
Area = (1/2) × Perimeter × Apothem
Or: Area = (1/4) × n × s² × cot(π/n)
Where n = sides, s = side length
Apothem = s / (2 × tan(π/n))
Distance from center to midpoint of any side
Interior = (n-2) × 180° / n
Sum of all interior angles = (n-2) × 180°
Exterior = 360° / n
All exterior angles sum to 360°
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A regular polygon is a closed 2D shape with all sides equal in length and all interior angles equal. Examples include equilateral triangles (3 sides), squares (4 sides), regular pentagons (5 sides), and hexagons (6 sides). The regularity makes calculations much simpler than irregular polygons.
The area formula is: Area = (1/4) × n × s² × cot(π/n), where n is the number of sides and s is the side length. Alternatively: Area = (1/2) × perimeter × apothem. For a hexagon with 6cm sides: Area = (1/4) × 6 × 36 × cot(π/6) = 93.53 cm².
The apothem is the distance from the center of a regular polygon to the midpoint of any side. Calculate it using: Apothem = s / (2 × tan(π/n)), where s is side length and n is number of sides. It's perpendicular to the side and essential for area calculations.
Interior angle = (n-2) × 180° / n, where n is the number of sides. Exterior angle = 360° / n. For a pentagon (5 sides): interior angle = (5-2) × 180 / 5 = 108°, exterior angle = 360 / 5 = 72°. These angles always sum to 180° for any polygon.
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