The circumference of a circular plot is 396 metres. what is the area of the circular plot?

### Concept & Area from Circumference We are given the outer boundary length. To find the enclosed space (area), we first isolate the radius from the circumference formula. $$ \text{Circumference} = 2\pi r $$ $$ \text{Area} = \pi r^2 $$ ### Step-by-Step Solution * Given: Circumference = $396\text{ m}$. * Set up equation: $2\pi r = 396 \Rightarrow 2 \times \frac{22}{7} \times r = 396$. * Simplify left side: $\frac{44}{7} \times r = 396$. * Solve for $r$: $r = \frac{396 \times 7}{44}$. * $44$ goes into $396$ exactly $9$ times: $r = 9 \times 7 = 63\text{ m}$. * Calculate Area: $\pi r^2 = \frac{22}{7} \times 63 \times 63$. * Simplify: $22 \times 9 \times 63 = 198 \times 63$. * Calculate final value: $198 \times 63 = 12474\text{ sq. m}$. ### Exam Strategy & Shortcut Instead of doing $198 \times 63$ the long way, treat $198$ as $(200 - 2)$. $63 \times (200 - 2) = 12600 - 126 = 12474$. This mental math trick dramatically reduces time and arithmetic errors. ### Common Pitfall Failing to square the radius when moving from circumference to area, or accidentally squaring the diameter instead. ### Final Answer Therefore, the correct answer is **12474 sq. m**.