It is known that perimeter of a flat figure is called length of the line limiting it. To find perimeter of a polygon it is enough to put lengths of its parties. For this purpose it is necessary to measure lengths of all pieces making it. If the regular polygon, then a problem of finding of perimeter much more becomes simpler.
It is required to you
- - ruler;
- - compasses.
Instruction
1. To find hexagon perimeter, measure and put lengths of all its six parties. Р = a1+ a2+ a3+ a4+ a5+ a6, where P – hexagon perimeter, and a1, a2 … a6 – lengths of its parties. Lead units of measure of each of the parties to one look – in this case will be to put only numerical values of lengths of the parties enough. The unit of measure of perimeter of a hexagon will coincide with unit of measure of the parties.
2. Example. There is a hexagon with lengths of parties of 1 cm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm. It is required to find its perimeter. Decision.1. The unit of measure of the first party (cm) differs from units of measure of lengths of other parties (mm). Therefore, translate: 1 cm = 10 mm.2. 10+2+3+4+5+6=30 (mm).
3. If a hexagon correct, then to find its perimeter, increase length of its party by six: Р = and * 6, where and – length of the party of the correct hexagon. Example. To find perimeter of the correct hexagon with a length of the party equal of 10 cm. Decision: 10 * 6 = 60 (cm).
4. The correct hexagon has unique property: radius of the circle described around such hexagon is equal to length of its party. Therefore if the radius of a circumscribed circle is known, to use a formula: P = R * 6 where R is the radius of a circumscribed circle.
5. Example. To calculate perimeter of the correct hexagon written in a circle with a diameter of 20 cm. Decision. Radius of a circumscribed circle will be equal: 20/2=10 (cm). Therefore, hexagon perimeter: 10 * 6 = 60 (cm).
6. If under the terms of a task the radius of an inscribed circle is set, then apply a formula: P = 4 * √3 * r where r is the radius of the circle entered in the correct hexagon.
7. If the area of the correct hexagon is known, then for calculation of perimeter use the following ratio: S = 3/2 * √3 * and² where S is the area of the correct hexagon. From here it is possible to find and = √ (2/3 * S/√3), therefore: Р = 6 * and = 6 * √ (2/3 * S/√3) = √ (24 * S/√3) = √ (8 * √3 * S) = 2 √ (2S√3).