By definition from planimetry a regular polygon is called the convex polygon at which the parties are equal among themselves and corners are also equal among themselves. The correct hexagon is a regular polygon, with number of the parties equal to six. There are several formulas for calculation of the area of a regular polygon.
Instruction
1. If the radius of the circle described about a polygon is known, then its area can be calculated on a formula: S = (n/2) • R²\• sin(2π/n) where n is number of the parties of a polygon, R is the radius of a circumscribed circle, π = 180º.В the correct hexagon all corners are equal 120 ° therefore the formula will have an appearance: S = √3 * 3/2 * R²
2. In case the circle with a radius of r is entered in a polygon, its area is calculated on a formula: S = N* r² * tg(π/n) where n is number of the parties of a polygon, r is the radius of an inscribed circle, π = 180º.Для a hexagon this formula takes a form: S = 2 * √3 * r²
3. The area of a regular polygon can also be calculated, knowing only length of its party on a formula: S = N*/4 a² * ctg(π/n), n is number of the parties of a polygon, an is length of the party of a polygon, π = 180º.Соответственно the area of a hexagon is equal: S = √3 * 3/2 * a²