Given: Area of square = 44 cm²
For a square with area 44 cm²:
side² = 44
side = √44
side = √(4 × 11)
side = 2√11 cm
The perimeter of the square:
Perimeter = 4 × side
Perimeter = 4 × 2√11
Perimeter = 8√11 cm
The circle has the same perimeter as the square.
Circumference of circle = 8√11 cm
Using the formula for circumference:
2πr = 8√11
r = 2π8√11
r = π4√11 cm
The area of the circle:
Area = πr²
Area = π × (π4√11)2
Area = π × π216×11
Area = π × π2176
Area = π176 cm²
Area = 3.14176 ≈ 56 cm²
Therefore, the area of the circle is 56 cm².