1. **Problem 1: Area of the ring-shaped shaded part** We have two circles: a large circle with radius $6$ m and a smaller inner circle with radius $4.1$ m. The shaded area is the area of the large circle minus the area of the smaller circle. Formula for the area of a circle: $$A = \pi r^2$$ Calculate the areas: - Large circle area: $$\pi \times 6^2 = 36\pi$$ - Small circle area: $$\pi \times 4.1^2 = 16.81\pi$$ Shaded area: $$36\pi - 16.81\pi = (36 - 16.81)\pi = 19.19\pi$$ Approximate using $\pi \approx 3.1416$: $$19.19 \times 3.1416 = 60.28$$ 2. **Problem 2: Area of the semicircle with diameter 9 m** Radius $r = \frac{9}{2} = 4.5$ m. Area of full circle: $$\pi r^2 = \pi \times 4.5^2 = 20.25\pi$$ Area of semicircle: $$\frac{1}{2} \times 20.25\pi = 10.125\pi$$ Approximate: $$10.125 \times 3.1416 = 31.80$$ 3. **Problem 3: Area of the rectangle with two semicircular cutouts** Rectangle area: $$9 \times 5.6 = 50.4$$ Each semicircle has diameter $5.6$ m, so radius $r = \frac{5.6}{2} = 2.8$ m. Area of one semicircle: $$\frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 2.8^2 = \frac{1}{2} \pi \times 7.84 = 3.92\pi$$ Two semicircles area: $$2 \times 3.92\pi = 7.84\pi$$ Approximate: $$7.84 \times 3.1416 = 24.63$$ Shaded area = rectangle area minus cutouts: $$50.4 - 24.63 = 25.77$$ **Final answers:** 1. $60.28$ m² 2. $31.80$ m² 3. $25.77$ m²