A regular hexagon is inscribed in a circle with a radius of 12 cm. Find the arc length of the circle

| May 11, 2021 | education

A regular hexagon is inscribed in a circle with a radius of 12 cm. Find the arc length of the circle corresponding to the central corner of the hexagon.

A regular hexagon is a hexagon in which all sides are equal. The vertices of such a polygon divide the circle circumscribed about it into equal parts. The length of the arc of a circle corresponding to the central corner of the hexagon can be found as one sixth of the length of the entire circle: l = 2πr / 6 = πr / 3 = π * 12/3 = 4π, which is approximately 12.566 cm.
2nd way: since in a regular hexagon all sides are equal, then the central angles are also equal. The total measure of the sum of all central angles is 360 degrees, so one central angle is 360/6 = 60 degrees. The length of the arc is determined by the formula: L = πra / 180, where a is the angle, r is the radius of the circle. L = π * 12 * 60/180 = π * 12/3 = 4π.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.