免费正多边形面积计算器
根据边数和边长计算正多边形的面积和周长。
面积
64.9519
公式
## Regular Polygon Formulas ### Area **Area = (n × s²) / (4 × tan(pi/n))** Alternatively: **Area = (1/2) × perimeter × apothem** ### Interior Angle **Interior angle = (n - 2) × 180 / n** degrees ### Apothem **Apothem = s / (2 × tan(pi/n))** The apothem is the distance from the center to the midpoint of a side.
计算示例
Regular hexagon with side length 5.
- 01Area = (6 × 25) / (4 × tan(pi/6)) = 150 / (4 × 0.5774) ≈ 64.9519
- 02Perimeter = 6 × 5 = 30
- 03Interior angle = (6-2) × 180/6 = 120°
- 04Apothem = 5 / (2 × 0.5774) ≈ 4.3301
常见问题
What is a regular polygon?
A regular polygon has all sides equal in length and all interior angles equal. Examples include equilateral triangles, squares, pentagons, and hexagons.
What is the apothem?
The apothem is the distance from the center of the polygon to the midpoint of any side. It is also the radius of the inscribed circle.
How does the interior angle change with more sides?
As the number of sides increases, the interior angle approaches 180 degrees. A triangle has 60°, a square 90°, a pentagon 108°, a hexagon 120°, etc.
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