Regular polygon (pentagon, hexagon, octagon…)
Area and perimeter, with the formula worked through and a drawing to scale.
Result
- Area
- 41.5692 sq ft
- = 41.5692 sq ft · 3.8619 m²
- Perimeter
- 24 ft
- = 24 ft · 7.3152 m
- Apothem (centre to mid-side)
- 3.4641 ft
- Radius (centre to corner)
- 4 ft
- Each interior angle
- 120°
- Mitre for each joint
- 30°
The working
Area: A = n s² ÷ (4 tan(180° ÷ n))
Perimeter: P = n s
A = 6 × 4² ÷ (4 × tan(180° ÷ 6)) = 41.5692 P = 6 × 4 = 24
Values in feet; areas in sq ft.
About the regular polygon (pentagon, hexagon, octagon…)
All sides and all angles equal: 5 = pentagon, 6 = hexagon, 8 = octagon (a gazebo floor). The apothem is the distance from the centre to the middle of a side.
Every formula on this site is explained step by step in Learn: area and perimeter.
Other shapes
Square Rectangle Parallelogram Rhombus Trapezoid (trapezium) Kite Triangle — three sides Triangle — base and height Right triangle Isosceles triangle Equilateral triangle Triangle — two sides and the angle between Circle Semicircle Quarter circle Sector (pie slice) Circular segment (arch) Ring (annulus) Ellipse (oval) L-shape Any polygon — by corner points