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Area of circles

Measurement

Japanese school year: Elementary 6

What you learn

Learn how to find the area of a circle by rearranging finely divided sectors into a shape close to a rectangle. This method applies to measuring circular flower beds, table surfaces, and pizza sizes. Prior understanding of pi and the area formula of parallelograms will make learning this concept smooth and intuitive.

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Key points

This formula finds the area S of a circle. Multiply radius r by itself, then multiply by pi π.

S=πr2S = \pi r^2

This formula finds the area S of a sector. Multiply the circle's area by the ratio of central angle θ to 360°.

S=πr2×θ360∘S = \pi r^2 \times \frac{\theta}{360^\circ}

This formula finds a sector's area S from its arc length ℓ and radius r. Multiply ℓ by r and divide by 2.

S=12ℓrS = \frac{1}{2}\ell r

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