Find the area of the circle and the length of the circumference of the circle if the side of the square circumscribed about it is 5√3cm.

The side of a square is equal to the diameter of a circle inscribed in it (a property of a circle inscribed in a square). The radius is half the diameter. D – diameter, R – radius.
L = side of the square = 5√3cm, R = D / 2 = 5√3cm / 2 = 5√3 / 2cm.
Circumference = 2 * pi * R = pi * D = 5√3 * pi cm (pi ~ 3.1415 …)
Area of a circle = pi * P ^ 2 = pi * (5√3 / 2) ^ 2 = 18.75 * pi cm.
Answer: circumference = 5√3 * pi cm, area of a circle = 18.75 * pi cm ^ 2.