A wire is bent to form a square of area 169 cm² . If the same wire is bent to form circle, then what is its area (in cm² , to the nearest whole number)?

Take $π = \frac{22}{7}$

215

Area of square = ( Side )²

169 = ( Side )²

Side = 13 cm

Now, Same wire that is used to form square is used to form circle.

So, Perimeter of square = Perimeter of Circle

Perimeter of square = 4 × Side = 4 × 13 = 52 cm

Now, Perimeter of circle = 2πR

= 2 × \(\frac{22}{7}\) × R

2 × \(\frac{22}{7}\) × R = 52

R = \(\frac{52  × 7 }{22 × 2 }\)

= \(\frac{91 }{11 }\)

Area of circle = πR²

= \(\frac{22}{7}\) × \(\frac{91 }{11 }\) × \(\frac{91 }{11 }\)

= 215.09 cm²