What is the circumference of the incircle of a square with area 36 cm^2

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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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`

Sources:
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llltkl | College Teacher | (Level 3) Valedictorian

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Let the side of the square be `x`

Its area: `x^2`

By the given condition:

`x^2=36 cm^2`

`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`

`=2*pi*3` cm

`=18.85` cm

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