The correct hexagon is the geometrical figure on the plane possessing six parties, equal in size. All corners at this figure are equal to 120 degrees. The area of the correct hexagon is very easily.
Instruction
1. Finding of the area of the correct hexagon is directly connected with one of its properties which says that around this figure it is possible to describe a circle, as well as to enter it in this hexagon. If in the correct hexagon entered a circle, then radius it it is possible to find on a formula: r = ((√3) *t)/2 where t is the party of this hexagon. It should be noted that the radius of the circle described around the correct hexagon is equal to its party (R = t).
2. Having understood as there is a radius of the entered / circumscribed circle, it is possible to start finding of the area of a required figure. For this purpose use the following formulas: S = (3 * √ 3*R²)/2; S = 2 * √ 3*r².
3. That finding of the area of this figure did not cause difficulties, we will review several examples. Example 1: The correct hexagon which party is equal to 6 cm is given, it is required to find its area. For the decision it is possible to use in several ways: S = (3 * √ 3*6²)/2 = 93.53 cm²Второй way longer. For a start find the radius of an inscribed circle: r = ((√3) *6)/2 = 5.19 smzaty use the second formula for finding of the area of the correct hexagon: S = 2 * √ 3*5.19² = 93.53 cm²Как are visible, both specified a way are valid and do not demand verification of the decisions.