A regular hexagon is inscribed in a circle of radius R. find its area.

univerkov | April 29, 2021 | education

Since the hexagon is regular, the chord AB contracts the arc equal to 360/6 = 60, then the triangle AOB is equilateral, OA = OB = AB = R.

The height OH of a regular triangle is: OH = AB * √3 / 2 = R * √3 / 2 cm.

Then Saov = AB * OH / 2 = R * R * √3 / 4 cm2.

Then the area of the hexagon is: S = 6 * Saov = R ^ 2 * 3 * √3 / 2 cm2.

Answer: the area of the hexagon is R ^ 2 * 3 * √3 / 2 cm2.

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.