The area of the square is s a) find the length of the inscribed circle b) the length of the arc between two adjacent

The area of the square is s a) find the length of the inscribed circle b) the length of the arc between two adjacent points of contact c) the area of the part of the square that lies outside the inscribed circle

Let the side of the square be x units long. It is known that the area of ​​a square is S. Then, since the area of ​​a square is found by the formula S = x ^ 2, the side x = S ^ (1/2). but). A circle is inscribed in the square. To find the length of the inscribed circle L, you need to determine its diameter d. Obviously, d = x = S ^ (1/2). We get, L = π ∙ d = π ∙ S ^ (1/2). b). The circle has four points of tangency with the square. Due to symmetry, the length of the arc between two adjacent points of contact will be one fourth of the circumference, that is, l = L / 4 = (π ∙ S ^ (1/2)) / 4. c) To find the area of ​​the part of the square Sv that lies outside the inscribed circle, you must first find the area of ​​the circle Sо. We find it by the formula Sо = (π ∙ d ^ 2) / 4 = (π ∙ S ^ (1/2) ^ 2) / 4 = π ∙ S / 4, and subtract it from the area of ​​the square: Sв = S – Sо = S – π ∙ S / 4 = S ∙ (4 – π) / 4.