Question

Perimeter of a square and circumference of a circle are equal. If the area of
the circle is 616 cm?, find the area of the square.

Answer 1

Area = 484 cm²

Step-by-step explanation:

Given:

Perimeter of a square & circumference of. circle are equal.

Area of circle is 616 cm².

To Find:

What is the area of square ?

Solution: Let the measure of each side of square be a cm.

As we know that

★ Area of Circle = πr² ★

➡ 616 = 22/7 × r²

➡ 616 ×7/22 = r²

➡ 56 × 7/2 = r²

➡ √28 × 7 = r

➡ √196 = r

➡ 14 cm = r

So measure of radius of circle is 14 cm. Now , Let's find the circumference of circle.

★ Circumference = 2πr ★

➮ 2 × 22/7 × 14

➮ 44 × 2 = 88 cm

★ Perimeter of Square = 4a ★

A/q

Perimeter = Circumference

⟹ 4 × a = 88

⟹ a = 88/4

⟹ a = 22 cm

★ Area of Square = a² ★

⟹ (22 × 22) cm²

⟹ 484 cm²

Hence, area of the square is 484 cm².

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Answer 2

Answer:

Step-by-step explanation:

Here we know that perimeter and circumference are equal , we want the area of the square.

First we have to find the radius of the circle

= 22/7 x r x r = 616 cm

=  r x r            = 616 cm x 7/22

=  r x r            = 196

= r                   =14 cm

Now we know that perimeter and circumference of a circle are equal .

we have to find circumference.

= 2 x 22/7 x 14 cm

= 88 cm

Now we have to find the side of the circle. We know that perimeter of a square = side x 4

s x 4 =88 cm

s      = 88/4

s       = 22 cm

area of a square = side x side

= 22 cm x 22 cm

= 484 cm