Subjects geometry

Perimeter Composite 3Bb223

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1. **State the problem:** We need to find the perimeter of a composite figure made of a rectangle and a semicircle attached to the right side of the rectangle. 2. **Identify given dimensions:** The rectangle has length 7 units and width 2 units. The semicircle has radius 2 units (same as the rectangle's width). 3. **Recall the perimeter formula for composite figures:** The perimeter is the sum of all outer edges. Here, it includes three sides of the rectangle (two lengths and one width) plus the curved edge of the semicircle. 4. **Calculate the semicircle's perimeter:** The circumference of a full circle is $$2\pi r$$, so the semicircle's curved edge is half of that: $$\pi r$$. 5. **Calculate the perimeter:** - Rectangle sides contributing: two lengths and one width: $$7 + 7 + 2 = 16$$ - Semicircle curved edge: $$\pi \times 2 = 2\pi$$ 6. **Sum the parts:** $$P = 16 + 2\pi$$ 7. **Approximate the value:** $$P \approx 16 + 2 \times 3.1416 = 16 + 6.2832 = 22.2832$$ 8. **Round to the nearest tenth:** $$P \approx 22.3$$ units. **Final answer:** The perimeter of the figure is approximately **22.3** units.