Subjects geometry

Kite Semicircle Perimeter F36A64

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1. **State the problem:** Find the perimeter of the given shape, which consists of a kite-like left section with two equal sides of 20 m each and a right semicircle with diameter 9 m. 2. **Formula for perimeter:** The perimeter of this shape is the sum of the kite's sides plus the semicircle's curved length. 3. **Kite sides:** The kite has two pairs of equal sides: two sides of 20 m and two sides of 9 m. 4. **Semicircle perimeter:** The semicircle's curved length is half the circumference of a full circle with diameter 9 m. 5. **Calculate semicircle length:** $$\text{Circumference} = \pi \times d = \pi \times 9 = 9\pi$$ $$\text{Semicircle length} = \frac{9\pi}{2}$$ 6. **Calculate total perimeter:** $$\text{Perimeter} = 20 + 20 + 9 + \frac{9\pi}{2} = 49 + \frac{9\pi}{2}$$ 7. **Approximate value:** Using $\pi \approx 3.1416$, $$\frac{9\pi}{2} \approx \frac{9 \times 3.1416}{2} = 14.137$$ $$\text{Perimeter} \approx 49 + 14.137 = 63.137\text{ m}$$ **Final answer:** $$\boxed{63.14\text{ m (approx.)}}$$
20 m20 m9 mSemicircle