Question

Диаметр окружности описанной около правильного шестиугольника равна 10 см вычислите периметр этого шести угольника

Answer 1

Длина окружности находится по формуле 2*π*r и равно это произведение 10. Получаем радиус окружности r=5/π,   В правильном шестиугольнике сторона равна радиусу описанной окружности, периметр равен 6*r.  P=30/π
Ответ:  30/π

Answer 2

Calculating the Perimeter of a Regular Hexagon

To calculate the perimeter of a regular hexagon, we can use the formula:

Perimeter = 6 * side length

Given that the diameter of the circle circumscribed around the regular hexagon is 10 cm, we can find the side length of the hexagon using the following steps:

1. Finding the Side Length of the Hexagon: - The diameter of the circumscribed circle is equal to the distance between two opposite vertices of the hexagon. - Using the formula for the diameter of a circumscribed circle, we can find the side length of the hexagon.

The formula for the diameter of the circumscribed circle of a regular hexagon is: d = 2 * side length

Solving for the side length: side length = d / 2

Substituting the given diameter (10 cm): side length = 10 / 2 = 5 cm.

2. Calculating the Perimeter: - Now that we have the side length, we can use the formula to find the perimeter of the regular hexagon.

Perimeter = 6 * 5 = 30 cm.

Therefore, the perimeter of the given regular hexagon is 30 cm.