A copper wire, when bent in the form of a square of encloses a region having 1089 sq cm. If the same wire is bent in the form of a circle, then find the area of the region enclosed by the wire.

The correct answer is 1386.

Let's solve the problem step-by-step by finding the length of the wire and then calculating the area of the circle formed by it.

Step 1: Find the side length of the square.
Let $s$ be the side length of the square.
The area of a square is given by the formula:
$\text{Area of square}=s^2$
We are given that the area of the square is 1089 sq cm. Therefore:
$s^2=1089$
Taking the square root on both sides:
$s=\sqrt{1089}=33\text{cm}$

Step 2: Find the length of the wire (perimeter of the square).
The total length of the wire is equal to the perimeter of the square.
$\text{Perimeter of square}=4·s$
$\text{Length of wire}=4·33=132\text{cm}$

Step 3: Find the radius of the circle.
If the same wire is bent to form a circle, the circumference of the circle will be equal to the length of the wire.
Let $r$ be the radius of the circle. The formula for the circumference of a circle is:
$\text{Circumference}=2·\pi ·r$
Setting this equal to the length of the wire (132 cm) and using $\pi \approx \frac{22}{7}$:
$2·\frac{22}{7}·r=132$
$\frac{44}{7}·r=132$
Multiplying both sides by $\frac{7}{44}$:
$r=132·\frac{7}{44}$
Since $132/44=3$:
$r=3·7=21\text{cm}$

Step 4: Calculate the area of the circle.
The area of a circle is given by the formula:
$\text{Area of circle}=\pi ·r^2$
Substituting $r=21\text{cm}$ and $\pi =\frac{22}{7}$:
$\text{Area}=\frac{22}{7}·{21}^2$
$\text{Area}=\frac{22}{7}·21·21$
$\text{Area}=22·3·21$
$\text{Area}=66·21=1386\text{sq cm}$

Thus, the area of the region enclosed by the wire when bent into a circle is 1386 sq cm.