Question

the perimeter of a square,whose side is 22cm,is the same as the circumference of a circle.Find the area of circle.​

Answer 1

Answer:

perimeter of square= 4a for any side 'a'

= 4×22

= 88 cm

A.T.Q

2•pi•r=88

pi•r =88/2

pi•r=44

$\frac{22}{7} \times r= 44$

$\frac{r}{7} = 44 \div 22$

$\frac{r}{7} = 2$

$r = 14$

Area of circle= 22/7 •r²

=22/7•196

=22×28

=616cm²

Answer 2

Given:

• Perimeter of square = Circumference of circle
• Side of square = 22 cm

To find:

• Area of circle

Solution:

Side of square = 22 cm

Perimeter of square = 4 × side

=> 4×22 cm

=> 88 cm

Perimeter of square = circumference of circle = 88 cm

therefore,

Circumference of circle = 2πr

$\sf \: 88 cm = 2 × \frac{22}{7} × r \\ \\ \sf r \: = \: \frac{88 \times 7}{2 \times 22} \\ \\ \sf \: r \: = \: \frac{ \cancel{88} \: ^{ \cancel{44}} \: ^{2} \times 7}{ \cancel2 \times \cancel{22}} \\ \\ \sf \: r \: = \: 14 \: cm$

$\sf \therefore Area \: of \: circle = πr² \\ \\ \sf \implies \: \frac{22}{7} \times 14 \times 14 \\ \\ \sf \implies \: \frac{22}{ \cancel{7}} \times \cancel{14} \: \: ^{2} \times 14 \\ \\ \boxed{ \red{\sf {\implies \: 616 \: {cm}^{2} }}}$