Respuesta :
Let's say that the length of the side of the square is a. The area of the square will be length^2 = a^2
Now the area of a circle is given by πr^2. If the area of the square and the circle are equal, we can say that a^2 = πr^2, therefor a = sq.root of (πr^2) = r*sq.root of π (as an exact answer), or 1.772r (to three decimal places)
Now the area of a circle is given by πr^2. If the area of the square and the circle are equal, we can say that a^2 = πr^2, therefor a = sq.root of (πr^2) = r*sq.root of π (as an exact answer), or 1.772r (to three decimal places)
Square is a parallelogram whose area is equal to the product of its sides. The circle is a plane figure whose area is calculated by the formula [tex]\pi[/tex]r².
The length of the side of the square is [tex]r\sqrt{\pi}[/tex].
Given:
The radius of the circle is = r cm.
Length of the side of square = a cm
Now,
Area of Square is = a²
Area of Circle = [tex]\pi[/tex]r²
Since, given that radius of a circle is equivalent to the length of the square, such that:
a² = [tex]\pi[/tex]r²
a² = [tex]\pi[/tex]r²
a = [tex]\sqrt{\pi r^2}[/tex]
a = [tex]r\sqrt{\pi}[/tex]
Thus, the value of the length of the square is [tex]r\sqrt{\pi}[/tex].
To know more about the area, refer to the following link:
https://brainly.com/question/1658516
