Subjects geometry

Circle Arcs E781E1

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1. **Problem statement:** Calculate the perimeter (omkretsen) of the figure composed of straight lines and quarter circle arcs. Each square side length is 0.5 cm. Round the answer to one decimal place. 2. **Understanding the figure:** The figure consists of straight segments and quarter circle arcs. The quarter circle arcs have radius equal to the side length of the squares, which is 0.5 cm. 3. **Formula for arc length:** The length of a quarter circle arc is given by $$\text{arc length} = \frac{1}{4} \times 2\pi r = \frac{\pi r}{2}$$ where $r$ is the radius. 4. **Calculate the arc length:** Given $r = 0.5$ cm, $$\text{arc length} = \frac{\pi \times 0.5}{2} = \frac{\pi}{4} \approx 0.7854 \text{ cm}$$ 5. **Calculate the total perimeter:** The figure has two quarter circle arcs and one straight segment of length 1.5 cm. Sum of arcs: $$2 \times 0.7854 = 1.5708 \text{ cm}$$ Add the straight segment: $$1.5708 + 1.5 = 3.0708 \text{ cm}$$ 6. **Rounding:** Rounded to one decimal place, $$3.0708 \approx 3.1 \text{ cm}$$ **Final answer:** The perimeter of the figure is approximately **3.1 cm**.