If area of a square is 44 cm², find the area of the circle formed by the same perimeter.

Given: Area of square = 44 cm²

For a square with area 44 cm²:

side² = 44

side = √44

side = √(4 × 11)

side = 2√11 cm

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The perimeter of the square:

Perimeter = 4 × side

Perimeter = 4 × 2√11

Perimeter = 8√11 cm

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The circle has the same perimeter as the square.

Circumference of circle = 8√11 cm

Using the formula for circumference:

2πr = 8√11

r = $\dfrac{8√11}{2π}$

r = $\dfrac{4√11}{π}$ cm

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The area of the circle:

Area = πr²

Area = π × $\left(\dfrac{4√11}{π}\right)^2$

Area = π × $\dfrac{16 × 11}{π²}$

Area = π × $\dfrac{176}{π²}$

Area = $\dfrac{176}{π}$ cm²

Area = $\dfrac{176}{3.14}$ ≈ 56 cm²

Therefore, the area of the circle is 56 cm².