Question

Найти площадь круга вписанного в правильный четырехугольник со стороной 10см

Answer 1

$S круга=\pi R^{2}=10\pi$

 

потомучто правильный четырех угольник-квадрат

Answer 2

сторона= диаметру круга вписанного в правильный четырехугольник

S=pi*r^2=pi*5 ^2=25pi

Answer 3

Finding the Area of a Circle Inscribed in a Regular Quadrilateral

To find the area of a circle inscribed in a regular quadrilateral with a side length of 10 cm, we need to determine the radius of the inscribed circle.

In a regular quadrilateral, each angle is 90 degrees, and the diagonals are equal in length and bisect each other at right angles. The diagonals of a regular quadrilateral are also the diameters of the inscribed circle.

To find the radius of the inscribed circle, we can use the Pythagorean theorem. Let's denote the radius as r and the side length of the quadrilateral as s (which is 10 cm in this case). The diagonal of the quadrilateral can be found using the formula:

diagonal = s * sqrt(2)

Since the diagonal is equal to twice the radius of the inscribed circle, we have:

2r = diagonal

Substituting the value of the diagonal, we get:

2r = s * sqrt(2)

Simplifying, we find:

r = (s * sqrt(2)) / 2

Now we can calculate the radius of the inscribed circle:

r = (10 cm * sqrt(2)) / 2

Using a calculator, we can find that the radius is approximately 7.071 cm.

To find the area of the circle, we use the formula:

Area = π * r^2

Substituting the value of the radius, we have:

Area = π * (7.071 cm)^2

Using a calculator, we can find that the area of the circle inscribed in the regular quadrilateral is approximately 157.08 square centimeters.

Please note that the calculations provided are approximate due to rounding.

Answer:

The area of the circle inscribed in a regular quadrilateral with a side length of 10 cm is approximately 157.08 square centimeters.