Question

Длина окружности описанной около квадрата равна 4 пи см. Найдите площадь квадрата.

Answer 1

C=4pi, C=2piR,   R=C/2pi=4pi/2pi=2 sm

Answer 2

Calculation of the Square's Area

To find the area of the square, we need to determine the length of its sides. Given that the circumference of the circle circumscribed around the square is equal to 4π cm, we can use this information to calculate the side length of the square.

The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius of the circle. Since the circle circumscribes the square, the diameter of the circle is equal to the diagonal of the square, which is equal to the side length multiplied by the square root of 2.

Let's denote the side length of the square as 'a'. Therefore, the diameter of the circle is 'a√2'. Given that the circumference of the circle is 4π cm, we can set up the following equation:

2πr = 4π,

where r is the radius of the circle. Since the radius is half the diameter, we have:

2π(a√2)/2 = 4π.

Simplifying the equation, we get:

a√2 = 4.

To find the side length of the square, we can isolate 'a' by dividing both sides of the equation by √2:

a = 4/√2.

Simplifying further, we get:

a = 2√2.

Now that we know the side length of the square is 2√2 cm, we can calculate its area. The area of a square is given by the formula: A = a^2, where A is the area and a is the side length.

Substituting the value of 'a' into the formula, we have:

A = (2√2)^2.

Simplifying, we get:

A = 4 * 2.

Therefore, the area of the square is 8 square cm.

Answer

The area of the square is 8 square cm.