Question

длина окружности описанной около квадрата равна 4п см. найдите площадь квадрата

Answer 1

Длина окружности равна 2пr. 

2пr = 4п

r = 2(см), тогда d = 4

d - диагональ квадрата. По теореме пифагора диагональ квадрата равна $a\sqrt{2}$ отсюда найдем а 

а = $\frac{4}{\sqrt{2}}$

тогда площадь равна = $\frac{16}{2} = 8$ см

Answer 2

Calculation of the Circumference of the Square

To find the circumference of a square, we can use the formula C = 4s, where C represents the circumference and s represents the length of one side of the square.

In this case, we are given that the circumference of the square is equal to 4π cm. Therefore, we can set up the equation as follows:

4s = 4π

To find the length of one side of the square, we divide both sides of the equation by 4:

s = π

Therefore, the length of one side of the square is π cm.

Calculation of the Area of the Square

To find the area of a square, we can use the formula A = s^2, where A represents the area and s represents the length of one side of the square.

In this case, we have already determined that the length of one side of the square is π cm. Therefore, we can substitute this value into the formula:

A = (π)^2

Simplifying the expression, we have:

A = π^2

Therefore, the area of the square is π^2 square cm.

Please note that the exact value of π is approximately 3.14159, so the area of the square is approximately 9.8696 square cm.

I hope this helps! Let me know if you have any further questions.