Question

Сторона правильного шестиугольника равна 10 см. Найти диаметр описанной вокруг него круга.

Answer 1

Если вокруг правильного шестиугольника описана окружность, то его сторона равна радиусу этой окружности, значит диаметр равен 20см.
Ответ: 20

Answer 2

Finding the Diameter of the Circumscribed Circle

To find the diameter of the circumscribed circle around a regular hexagon, we can use the fact that the diameter is equal to twice the apothem of the hexagon. The apothem is the distance from the center of the hexagon to any of its sides.

Given that the side length of the hexagon is 10 cm, we need to find the apothem.

Using the information from the search results, we can find the apothem by calculating the value of AC in the following equation:

AC = (side length) / (2 * tan(180° / 6)) Substituting the given side length of 10 cm into the equation, we get:

AC = 10 / (2 * tan(30°))

Calculating the value of the tangent of 30°, we find that tan(30°) = 0.5774.

Substituting this value into the equation, we have:

AC = 10 / (2 * 0.5774) = 8.6603 cm

Therefore, the apothem of the hexagon is approximately 8.6603 cm.

To find the diameter of the circumscribed circle, we multiply the apothem by 2:

Diameter = 2 * AC = 2 * 8.6603 = 17.3206 cm

Therefore, the diameter of the circumscribed circle around the hexagon is approximately 17.3206 cm.

Please note that the calculations are based on the assumption that the hexagon is a regular hexagon, where all sides and angles are equal.