Question

The area of a square is 121cm. if the perimeter of the square is equal to the circumference of a circle. find the area of the circle
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Answer 1

Answer:

$area \: of \: square = side\times side \\ 121 = {side}^{2} \\ \sqrt{121} = side \\ 11 = side \\ perimeter \: of \: square = 4 \times side \\perimeter = 4 \times 11 \\ perimeter = 44 \\ perimeter = circumference \\ circumference \: of \: circle = 2\pi \: r \\ 44= 2 \times \frac{22}{7} \times r \\ \frac{44 \times 7}{2 \times 22} = r \\ 7 = radius \\ area \: o$

$area \: of \: square = side\times side \\ 121 = {side}^{2} \\ \sqrt{121} = side \\ 11 = side \\ perimeter \: of \: square = 4 \times side \\perimeter = 4 \times 11 \\ perimeter = 44 \\ perimeter = circumference \\ circumference \: of \: circle = 2\pi \: r \\ 44= 2 \times \frac{22}{7} \times r \\ \frac{44 \times 7}{2 \times 22} = r \\ 7 = radius \\ area \: of \: circle = \pi {r}^{2} \\ area = \frac{22}{7} \times 7 \times 7 \\ area = 154 {cm}^{2}$

Answer 2

Given :-

Area of square is =121 cm²

To Calculate :-

Area of the circle

Solution :-

We know area of square is = a²

On equating,

==> a² = 121 sq.cm

==> a = 11cm

And;

Perimeter of square = 4a

Perimeter of square = 4 × 11

Perimeter of square = 44 cm

Also we know that;

Circumference of circle is =2πr

According the question :-

Circumference of circle = perimeter of square

Therefore,

==> 2 πr = 44cm

==> 2 × 22/7 × r = 44cm

==> r = (44 x 7) / 7

==> r = 7cm

Area of circle = πr²

==> Area of circle = 22/7 × 7 × 7

==> Area of the circle = 154 sq.cm

Hence :-

Area of the circle is 154 cm².