Sectors

Japanese school year: Junior high 1

What you learn

Learn how to calculate the arc length and area of a sector using its radius and central angle. This topic builds on the formulas for the circumference and area of a circle using ratios. It is widely used in geometric measurement, such as unfolding solids and finding composite areas.

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Key points

This formula is used to calculate the arc length $l$ of a sector. It multiplies the entire circle's circumference ( $2\pi r$ , for radius $r$ ) by the fraction of the central angle $x$ over $360^\circ$ .

l = 2\pi r \times \frac{x}{360}

This formula is used to calculate the area $S$ of a sector. It multiplies the entire circle's area ( $\pi r^2$ , for radius $r$ ) by the fraction of the central angle $x$ over $360^\circ$ .

S = \pi r^2 \times \frac{x}{360}

This formula is used to find the sector area $S$ from the arc length $l$ and radius $r$ without knowing the central angle. It is calculated similarly to a triangle's area (base $\times$ height $\div 2$ ).

S = \frac{1}{2}lr

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Practice 1Coming soon