once a circle is inscribed in a square , the diameter of the circle is same to the side size of the square.

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girlfriend can uncover the perimeter and also area of the square, when at the very least one measure of the circle or the square is given.

because that a square v side size s , the complying with formulas room used.

Perimeter = 4 s

Area = s 2

diagonal = s 2

Similarly, girlfriend can discover the one and also area the the circle , when at the very least one measure of the circle or the square is given.

for a circle through radius r , the adhering to formulas are used.

circumference = 2 π r

Area = π r 2


instance 1:

discover the perimeter the the square.

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once a one is inscribed in a square, the diameter of the one is equal to the side length of the square.

So, the side length of the square is 6 cm.

The perimeter ns that a square v side length s is provided by ns = 4 s .

substitute 6 because that s in p = 4 s .

ns = 4 ( 6 )           = 24

The perimeter that the square is 24 cm.


instance 2:

What is the area the a circle that is inscriptions in a square the area 64 square units?

once a circle is inscribed in a square, the size of each side the the square is same to the diameter the the circle. That is, the diameter the the inscribed circle is 8 units and also therefore the radius is 4 units.

The area that a one of radius r units is A = π r 2 .

substitute r = 4 in the formula.

A = π ( 4 ) 2           = 16 π           ≈ 50.24

Therefore, the area that the inscribe circle is about 50.24 square units.


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