Each side of a square formed by a wire is 14 cm. The area of the circle that can be formed by this wire is :

1. 144 cm²

2. 154 cm²

3. 164 cm²

4. 249.45 cm²

Given,

Each side of a square formed by a wire is 14 cm.

Total length of wire = Perimeter of square = 4 × 14 = 56 cm.

The circle formed with the wire will be having the circumference = 56 cm.

Let radius of circle be r cm.

2πr = 56

r = $\dfrac{56}{2π} = \dfrac{28}{π}$

Area of circle = πr²

$= \pi \times \left(\dfrac{28}{π}\right)^2 \\[1em] = \pi \times \dfrac{28}{π} \times \dfrac{28}{π} \\[1em] = \dfrac{28 \times 28}{π} \\[1em] = \dfrac{28 \times 28}{\dfrac{22}{7}} \\[1em] = \dfrac{28 \times 28 \times 7}{22} \\[1em] = 249.45 \text{ cm}^2$

Hence, option 4 is the correct option.