Regular Polygon Calculator
Area
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Perimeter
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Interior Angle
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Apothem
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Properties of Regular Polygons
Interior angle = (n-2)*180/n. Hexagon: 120 degrees. Apothem = s/(2*tan(pi/n)).
Area = (1/2)*n*s*apothem. As sides increase, polygon approaches a circle.
Found in architecture (stop signs), nature (honeycombs), and engineering (nuts and bolts).
Frequently Asked Questions
Interior angle formula?
(n-2)*180/n. Triangle: 60. Square: 90. Pentagon: 108. Hexagon: 120. Octagon: 135.
What is apothem?
Perpendicular distance from center to midpoint of any side. = s/(2*tan(pi/n)).
Exterior angle?
360/n. Hexagon: 60. Exterior angles of any convex polygon sum to 360.
Which tile a plane?
Only equilateral triangles, squares, and regular hexagons (60, 90, 120 degrees divide 360).