Subjects geometry

Walkway Area B2Ac69

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1. **State the problem:** We need to find the area of a walkway formed by four semicircles. The inner semicircles have a diameter of 14 metres, and the walkway width between the inner and outer semicircles is 2 metres. 2. **Identify the radii:** - Inner semicircle radius $r_i = \frac{14}{2} = 7$ metres. - The width of the walkway is 2 metres, so the outer semicircle radius $r_o = 7 + 2 = 9$ metres. 3. **Formula for the area of a semicircle:** $$\text{Area} = \frac{1}{2} \pi r^2$$ 4. **Calculate the total area of the four outer semicircles:** $$4 \times \frac{1}{2} \pi r_o^2 = 2 \pi (9^2) = 2 \pi \times 81 = 162 \pi$$ 5. **Calculate the total area of the four inner semicircles:** $$4 \times \frac{1}{2} \pi r_i^2 = 2 \pi (7^2) = 2 \pi \times 49 = 98 \pi$$ 6. **Find the area of the walkway by subtracting inner area from outer area:** $$\text{Area of walkway} = 162 \pi - 98 \pi = (162 - 98) \pi = 64 \pi$$ 7. **Final answer:** $$\boxed{64 \pi \text{ square metres}}$$ This is the area of the walkway formed by the four semicircles.