1. **Problem:** Find the perimeter and area of a polygon with sides 12 in, 6.4 in, 4.6 in, 9 in, and 9 in. 2. **Formula:** - Perimeter $P$ is the sum of all side lengths: $$P = \text{sum of sides}$$ - Area $A$ depends on the shape; assuming a polygon, use decomposition or given data (not provided here, so we calculate perimeter only). 3. **Perimeter calculation:** $$P = 12 + 6.4 + 4.6 + 9 + 9 = 41\text{ in}$$ 4. **Area:** Not enough information to calculate area precisely. --- 1. **Problem:** Find the perimeter and area of a polygon with sides 5.5 m, 6 m, 14 m, and 9 m. 2. **Perimeter formula:** $$P = \text{sum of sides}$$ 3. **Perimeter calculation:** $$P = 5.5 + 6 + 14 + 9 = 34.5\text{ m}$$ 4. **Area:** Not enough information to calculate area precisely. --- 1. **Problem:** Find the perimeter and area of a composite figure with a semicircle of diameter 12 yd and polygon sides 22.3 yd, 14 yd, and 11 yd. 2. **Formulas:** - Semicircle perimeter (half circumference plus diameter): $$P_{semi} = \pi r + d$$ where $r = \frac{d}{2} = 6$ yd, $d=12$ yd. - Area semicircle: $$A_{semi} = \frac{\pi r^2}{2}$$ - Total perimeter is sum of polygon sides plus semicircle arc (excluding diameter counted twice). 3. **Calculations:** - Semicircle arc length: $$\pi r = 3.14 \times 6 = 18.84\text{ yd}$$ - Total perimeter: $$P = 22.3 + 14 + 11 + 18.84 = 66.14\text{ yd}$$ - Area semicircle: $$A_{semi} = \frac{3.14 \times 6^2}{2} = \frac{3.14 \times 36}{2} = 56.52\text{ yd}^2$$ - Area polygon not given, so total area unknown. --- 1. **Problem:** Find the perimeter and area of a rounded composite figure with vertical 20 cm and horizontal 21 cm. 2. **Assumption:** Figure is a rectangle with a semicircle on one side (common in such problems). 3. **Formulas:** - Perimeter: sum of rectangle sides plus semicircle arc minus diameter counted twice. - Semicircle radius: $$r = \frac{21}{2} = 10.5\text{ cm}$$ - Semicircle arc length: $$\pi r = 3.14 \times 10.5 = 32.97\text{ cm}$$ - Rectangle perimeter without one side (diameter): $$2 \times 20 + 21 = 61\text{ cm}$$ - Total perimeter: $$61 + 32.97 = 93.97\text{ cm}$$ - Area rectangle: $$20 \times 21 = 420\text{ cm}^2$$ - Area semicircle: $$\frac{3.14 \times 10.5^2}{2} = \frac{3.14 \times 110.25}{2} = 173.09\text{ cm}^2$$ - Total area: $$420 + 173.09 = 593.09\text{ cm}^2$$