1. **Problem statement:** Calculate the area and perimeter of each given polygon. --- ### a) Rectangle (12 cm × 6 cm) 1. Formula for area: $$A = \text{length} \times \text{width}$$ 2. Formula for perimeter: $$P = 2 \times (\text{length} + \text{width})$$ 3. Calculate area: $$A = 12 \times 6 = 72$$ cm² 4. Calculate perimeter: $$P = 2 \times (12 + 6) = 2 \times 18 = 36$$ cm --- ### b) Rhombus (diagonals 8 cm and 4 cm, side length 4.5 cm) 1. Formula for area of rhombus: $$A = \frac{d_1 \times d_2}{2}$$ where $d_1$ and $d_2$ are diagonals 2. Formula for perimeter: $$P = 4 \times \text{side}$$ 3. Calculate area: $$A = \frac{8 \times 4}{2} = \frac{32}{2} = 16$$ cm² 4. Calculate perimeter: $$P = 4 \times 4.5 = 18$$ cm --- ### c) Parallelogram (base 9 cm, side 17 cm, height 12 cm) 1. Formula for area: $$A = \text{base} \times \text{height}$$ 2. Formula for perimeter: $$P = 2 \times (\text{base} + \text{side})$$ 3. Calculate area: $$A = 9 \times 12 = 108$$ cm² 4. Calculate perimeter: $$P = 2 \times (9 + 17) = 2 \times 26 = 52$$ cm --- ### d) Pentagon (sides: 25 cm, 14 cm, 20.5 cm, 42.5 cm, interior dashed length 18 cm) 1. Since no height or apothem is given, and the shape is irregular, we approximate perimeter by summing all sides. 2. Perimeter: $$P = 25 + 14 + 20.5 + 42.5 + 18 = 120$$ cm 3. Area is not directly computable with given data; no height or apothem provided. --- ### e) Triangle (base 8 cm, sides 20 cm and 11 cm, height 3 cm) 1. Formula for area: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 2. Formula for perimeter: $$P = \text{side}_1 + \text{side}_2 + \text{base}$$ 3. Calculate area: $$A = \frac{1}{2} \times 8 \times 3 = 12$$ cm² 4. Calculate perimeter: $$P = 20 + 11 + 8 = 39$$ cm --- ### f) Triangle (left side 9 cm, base 18 cm, slanted side 20 cm) 1. No height given, so area calculation requires Heron's formula. 2. Calculate semi-perimeter: $$s = \frac{9 + 18 + 20}{2} = \frac{47}{2} = 23.5$$ cm 3. Heron's formula for area: $$A = \sqrt{s(s - a)(s - b)(s - c)}$$ 4. Calculate area: $$A = \sqrt{23.5(23.5 - 9)(23.5 - 18)(23.5 - 20)} = \sqrt{23.5 \times 14.5 \times 5.5 \times 3.5}$$ 5. Calculate inside the root: $$23.5 \times 14.5 = 340.75$$ $$5.5 \times 3.5 = 19.25$$ $$340.75 \times 19.25 = 6554.9375$$ 6. Area: $$A = \sqrt{6554.9375} \approx 81$$ cm² 7. Perimeter: $$P = 9 + 18 + 20 = 47$$ cm --- ### g) Kite (horizontal diagonal 37 cm, vertical diagonal 24 cm, side lengths 17 cm and 28 cm) 1. Formula for area of kite: $$A = \frac{d_1 \times d_2}{2}$$ 2. Formula for perimeter: $$P = 2 \times (\text{side}_1 + \text{side}_2)$$ 3. Calculate area: $$A = \frac{37 \times 24}{2} = \frac{888}{2} = 444$$ cm² 4. Calculate perimeter: $$P = 2 \times (17 + 28) = 2 \times 45 = 90$$ cm --- **Final answers:** - a) Area = 72 cm², Perimeter = 36 cm - b) Area = 16 cm², Perimeter = 18 cm - c) Area = 108 cm², Perimeter = 52 cm - d) Perimeter = 120 cm (area not computable with given data) - e) Area = 12 cm², Perimeter = 39 cm - f) Area ≈ 81 cm², Perimeter = 47 cm - g) Area = 444 cm², Perimeter = 90 cm