The area of the circle is 64π.
Step-by-step explanation:
It is given that, the square has an area of 64 square centimeters.
The circle inscribed in the square is tangent to the square at A, B, C, and D.
This means that, the radius of the circle is same as the length of the side of the square.
To find the length of the side of the square :
Let, the length of the side of square is 'a'.
Area of the square = a²
⇒ 64 = a²
Taking square root on both sides,
⇒ a = ± 8
Since, length cannot be negative. The side of the square is 8 centimeters.
Therefore, the radius of the circle = 8 cm.
To find the area of the circle :
The formula to find the area of the circle is given by,
Area of the circle = πr²
⇒ π×8²
⇒ π× 8× 8
⇒ 64π
Therefore, the area of the circle is 64π.
