Question

A wire is in a circular shape of area $5544{cm}^2$. If the same wire is bent in the shape of square. Find the length of a side of the square and its area.

Answer 1

The area of circular shape is

$5544c{m}^2$

$\pi r^2=5544$

$\frac{22}{7}{r}^2=5544$

$r^2=5544\times \frac{7}{22}$

$r^2=252\times 7$

$r^2=1764$

$r=\sqrt{1764}$

$r=42$

The circumference of circle

$=2\pi r$

$=2\times \frac{22}{7}\times 42$

$=2\times 22\times 7$

$=154cm$

Now, The perimeter of square is

$154cm$

Let the side be $a$,

$\therefore 4a=154$

$a=\frac{77}{2}$

Area of square

$a^2$ $={\left(\frac{77}{2}\right)}^2$

$=\frac{5929}{4}$