If the perimeter of a circular field is 132 m, what is the total area of the field (in sq. m)?

The correct answer is 1386.

Step 1: Find the radius of the circular field.

The perimeter (circumference) of a circular field is given by the formula:

$P=2\pi r$

Where:
- $P$ is the perimeter (132 m)
- $r$ is the radius of the circular field
- $\pi =\frac{22}{7}$

Substituting the given values into the formula:

$132=2\times \frac{22}{7}\times r$

$132=\frac{44}{7}\times r$

Solving for $r$:

$r=132\times \frac{7}{44}$

$r=3\times 7=21\text{m}$

Step 2: Calculate the total area of the field.

The area of a circular field is given by the formula:

$A=\pi r^2$

Substituting $r=21\text{m}$ and $\pi =\frac{22}{7}$:

$A=\frac{22}{7}\times 21\times 21$

$A=22\times 3\times 21$

$A=66\times 21=1386\text{sq. m}$

Thus, the total area of the field is 1386 sq. m.