1. The problem involves calculating the area or perimeter of various circle sectors and a triangle based on given radii and dimensions. 2. The formulas for circle sectors are: - Area of a full circle: $$A = \pi r^2$$ - Area of a semicircle: $$A = \frac{1}{2} \pi r^2$$ - Area of a quarter circle: $$A = \frac{1}{4} \pi r^2$$ - Area of a three-quarter circle: $$A = \frac{3}{4} \pi r^2$$ 3. For the triangle formed by radius lines (right triangle), the area is: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. Convert all measurements to meters for consistency: - 2.5 cm = 0.025 m - 0.79 (assumed meters) - 4.5 cm = 0.045 m - 24 m (already in meters) - 2.2 cm = 0.022 m - 8.4 cm = 0.084 m - 0.1 m (already meters) - 10.99 cm = 0.1099 m - 1.57 dm = 0.157 m - 21.98 cm = 0.2198 m - 56.52 mm = 0.05652 m 5. Calculate areas: - a) Full circle with radius 0.025 m: $$A = \pi \times (0.025)^2 = \pi \times 0.000625 = 0.0019635\, m^2$$ - b) Semicircle with radius 0.045 m: $$A = \frac{1}{2} \pi (0.045)^2 = \frac{1}{2} \pi \times 0.002025 = 0.00318\, m^2$$ - c) Quarter circle with radius 0.022 m: $$A = \frac{1}{4} \pi (0.022)^2 = \frac{1}{4} \pi \times 0.000484 = 0.00038\, m^2$$ - d) Quarter circle with radius 0.084 m: $$A = \frac{1}{4} \pi (0.084)^2 = \frac{1}{4} \pi \times 0.007056 = 0.00555\, m^2$$ - e) Three-quarter circle with radius 0.1 m: $$A = \frac{3}{4} \pi (0.1)^2 = \frac{3}{4} \pi \times 0.01 = 0.02356\, m^2$$ - f) Right triangle with base 0.1099 m and height 0.157 m: $$A = \frac{1}{2} \times 0.1099 \times 0.157 = 0.00863\, m^2$$ 6. Final answers: - a) 0.00196 m² - b) 0.00318 m² - c) 0.00038 m² - d) 0.00555 m² - e) 0.02356 m² - f) 0.00863 m² These calculations show the areas of the given shapes based on their radii and dimensions.