Subjects geometry

Figure Eight Area

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Figure Eight Area


1. The problem asks to calculate the area of a shape formed by two quarter circles, each with radius 2 cm, combined to form a figure-eight or hourglass shape. 2. Each quarter circle has radius $r = 2$ cm. 3. The area of a full circle is given by the formula $$A = \pi r^2$$. 4. Since each quarter circle is one-fourth of a full circle, the area of one quarter circle is $$\frac{1}{4} \pi r^2 = \frac{1}{4} \pi (2)^2 = \frac{1}{4} \pi \times 4 = \pi$$ cm². 5. The shape consists of two such quarter circles, so the total area is $$2 \times \pi = 2\pi$$ cm². 6. Therefore, the area of the shape is $$2\pi$$ cm².