To find the circumference of the circle inscribed in a square of 36 cm^2, first find the length of the side of the square.
Since area of a square is found by `A = s^2` solve for s, when A = 36
`36 = s^2`
`sqrt(36) = s`
`s = 6`
The side length of the square is 6 cm. The circle that is inscribed in this circle will have a diameter that is the same length as the length of the side of the square. Therefore, the diameter of the circle is also 6 cm.
Since the diameter is 6 cm, the radius is half of the diameter, which makes the radius 3 cm.
To find the circumference of a circle with radius equal to 3 use the formula:
`C = 2pir`
`C = 2pi* 3`
`C = 6pi`
The circumference of a circle inscribed in a square with area 36 is `6pi cm` or `18.85 cm`
Let the side of the square be `x`
Its area: `x^2`
By the given condition:
`x=sqrt(36 cm^2)=6 cm`
The diameter of the in-circle is thus `x` .
Radius`=x/2=6/2` , i.e. `3 ` cm
Circumference of the in-circle: `= 2 *pi* r`