Question

perimeter of a square and circumference of a circle are equal if the area of the square is 484 CM square find the area of the circle

Answer 1

Side of square = √ area

                        = √484 = 22 cm

Circumference of circle = 22 × 4 cm

⇒ 2πr = 22 × 4

⇒ r = 7 ×2

∴ r = 14 cm

Area of circle = πr² = 196π = 616 cm²

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Answer 2

Given :-

Area of square = 484cm²

To find :-

Area of the circle

Solution :-

We know area of square is = a²

On equating,

a² = 484sq.cm

a = 22cm

Perimeter of square = 4a

==> Perimeter of square = 4a = 4×22

==> Perimeter of square = 88cm

Circumference of circle = 2πr

According to Question :-

Circumference of circle = perimeter of square is given

Therefore :-

==> 2πr = 88cm

==> 2×22/7×r = 88cm

==> r = 14cm

Now :-

Area of circle = πr²

Area of circle = 22/7×14×14

Area of circle = 616sq.cm

Hence:-

Area of the circle is 616 cm².