The Circle Area Slice Trick

Want to find the area of a sector (slice) of a circle *without* memorizing a new formula? It's easier than you think!

Subject: geometry • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

Instead of using the sector area formula, use proportions! Find the fraction of the *whole* circle represented by the sector's central angle. Then, multiply this fraction by the area of the whole circle. Why? A sector is simply a *fraction* of the whole circle. If the central angle is $\theta$ (in degrees), the fraction is $\frac{\theta}{360}$. Thus, Sector Area = $\frac{\theta}{360} \times \pi r^2$, where $r$ is the radius.

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