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

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.

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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