Question

найдите периметр правильного шестиугольника вписанного в окружность, если дуга, стягиваемая его стороной, равна П см.​

Answer 1

Ответ:

Периметр равен 18 см

Объяснение:

Дуга, стягиваемая стороной правильного шестиугольника равна L = π см, что соответствует центральному углу α = 60° = π/3.

Длина дуги

L = α · R

Откуда радиус окружности

R = L : α = π : (π/3) = 3 (см)

Сторона вписанного шестиугольника равна радиусу окружности

a = R = 3 см

Периметр шестиугольника

Р = 6а = 6 · 3 = 18 (см)

 

Answer 2

Perimeter of a Regular Hexagon Inscribed in a Circle

To find the perimeter of a regular hexagon inscribed in a circle, we need to know the length of the arc formed by one of its sides. Let's call this length "P" in centimeters.

A regular hexagon has six equal sides, and each interior angle measures 120 degrees. The hexagon is inscribed in a circle, which means that each vertex of the hexagon lies on the circumference of the circle.

To find the perimeter of the hexagon, we can use the fact that the length of the arc formed by one side is equal to the circumference of the circle divided by 6. Therefore, we can calculate the circumference of the circle and then divide it by 6 to find the length of one side.

The formula for the circumference of a circle is given by:

C = 2πr

Where: - C is the circumference of the circle, - π is a mathematical constant approximately equal to 3.14159, - r is the radius of the circle.

Since the hexagon is inscribed in the circle, the radius of the circle is equal to the distance from the center of the circle to one of its vertices. This distance is also equal to the length of one of the hexagon's sides.

Let's calculate the perimeter of the hexagon using the given length of the arc "P" in centimeters.

Calculation:

1. Calculate the circumference of the circle: - We know that the length of the arc formed by one side of the hexagon is equal to "P" centimeters. - The circumference of the circle is equal to 6 times the length of the arc, since there are 6 sides in a hexagon. - Therefore, the circumference of the circle is 6P centimeters.

2. Calculate the length of one side of the hexagon: - Since the hexagon is inscribed in the circle, the length of one side is equal to the radius of the circle. - The radius of the circle is equal to half of its circumference divided by π. - Therefore, the length of one side of the hexagon is (6P / (2π)) centimeters.

3. Calculate the perimeter of the hexagon: - The perimeter of the hexagon is equal to 6 times the length of one side, since there are 6 sides in a hexagon. - Therefore, the perimeter of the hexagon is 6 * (6P / (2π)) centimeters.

Answer:

The perimeter of the regular hexagon inscribed in a circle, given that the length of the arc formed by one side is "P" centimeters, is 6 * (6P / (2π)) centimeters.

Please note that the exact value of the perimeter depends on the specific value of "P" given in the question.

Let me know if there's anything else I can help you with!