Question

a steel wire when bent to form a square encloses an area of 121 cm² .if the same wire is bent to form a circle find the area of the circle​

Answer 1

Area of square = 121 $cm^{2}$

so the area of square =$\sqrt{a}$

              $\sqrt{a}$ = 121

               a = $\sqrt{121}$

               a = 11 cm

∴ the side of square = 11 cm

Perimeter of the square =4× side

                                        =4× 11

                                      =44 cm

                                      =length of the wire

∴circumference of circle = length of wire

                                        = 44 cm

let the radius of wire "r"

with the help of circumference we can find the radius of circle.

2πr = 44

2×22/7×r = 44

r = 44 × 7 / 2×22

= 7 cm

Now we have the radius of circle we can easily calculate the area of circle which is asked in question.

Area of the circle = π $r^{2}$

                             = 22/7 ×7²

                             = 154 cm²