Subjects geometry

Perimeter Semicircles 8Ae306

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1. **Problem Statement:** Find the perimeter of a figure composed of two semicircles with radius 2 cm each, adjacent to each other. 2. **Formula for circumference of a circle:** $$C = 2 \pi r$$ For a semicircle, the perimeter (arc length) is half of the full circle's circumference: $$\text{Semicircle perimeter} = \pi r$$ 3. **Given:** Radius $r = 2$ cm Pi approximated as $\pi = 3$ 4. **Calculate the perimeter of each semicircle:** $$\text{Perimeter of one semicircle} = \pi r = 3 \times 2 = 6 \text{ cm}$$ 5. **Total perimeter of the figure:** The figure's perimeter consists of the outer arcs of both semicircles plus the straight line segment between their bases. Since the two semicircles are adjacent, the straight line segment between their bases is equal to the diameter of one semicircle: $$\text{Diameter} = 2r = 4 \text{ cm}$$ The total perimeter is: $$P = \text{arc of larger semicircle} + \text{arc of smaller semicircle} + \text{straight line segment}$$ $$P = 6 + 6 + 4 = 16 \text{ cm}$$ **Final answer:** $$\boxed{16 \text{ cm}}$$