Question

Найдите площадь круга вписанного в правильный шестиугольник со стороной а

Answer 1

смотри  прикреплённый файл

Answer 2

Calculating the Area of a Circle Inscribed in a Regular Hexagon

To find the area of a circle inscribed in a regular hexagon with side length 'a', we can use the following steps:

1. Find the radius of the inscribed circle: - The radius of the inscribed circle is equal to half the length of the apothem of the hexagon. - The apothem of a regular hexagon is the distance from the center of the hexagon to the midpoint of any side. - The apothem can be calculated using the formula: apothem = (side length of hexagon) / (2 * tan(π/6)).

2. Calculate the area of the inscribed circle: - The area of a circle is given by the formula: area = π * (radius)^2.

Let's calculate the area of the circle inscribed in a regular hexagon with side length 'a' step by step.

Step 1: Finding the Radius of the Inscribed Circle

The apothem of a regular hexagon with side length 'a' can be calculated using the formula: apothem = (side length of hexagon) / (2 * tan(π/6)).

In this case, the side length of the hexagon is 'a', so the apothem can be calculated as follows:

apothem = a / (2 * tan(π/6)).

Step 2: Calculating the Area of the Inscribed Circle

The area of a circle is given by the formula: area = π * (radius)^2.

In this case, the radius of the inscribed circle is equal to half the length of the apothem.

Let's substitute the value of the radius into the formula to calculate the area:

area = π * (radius)^2.

Please note that the value of 'a' is not provided in the question, so we cannot provide a specific numerical answer. However, the above steps outline the process to calculate the area of a circle inscribed in a regular hexagon with side length 'a'.