1. **Calculate the area of each shape** (i) L-shaped polygon made of rectangles: - Break into two rectangles: - Rectangle A: $12\text{ mm} \times 7\text{ mm} = 84\text{ mm}^2$ - Rectangle B: $3\text{ mm} \times 5\text{ mm} = 15\text{ mm}^2$ - Total area = $84 + 15 = 99\text{ mm}^2$ (ii) Right triangle with perpendicular sides 8 cm and 6 cm: - Area formula for triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - Substitute values: $$\text{Area} = \frac{1}{2} \times 8 \times 6 = 24\text{ cm}^2$$ 2. **Determine the net area of the shape with a hole** - Outer rectangle area: $8\text{ in} \times 11\text{ in} = 88\text{ in}^2$ - Hole (square) area: $3\text{ in} \times 3\text{ in} = 9\text{ in}^2$ - Net area = Outer area $-$ Hole area = $88 - 9 = 79\text{ in}^2$ 3. **Determine the area of the parallelogram-like shape** - Area formula for parallelogram: $$\text{Area} = \text{base} \times \text{height}$$ - Given base = $10.2\text{ yd}$, height = $3.7\text{ yd}$ (height is perpendicular distance) - Area = $10.2 \times 3.7 = 37.74\text{ yd}^2$ 4. **Calculate the total area of the flowerbed (triangle + rectangle)** - Rectangle area: $9\text{ ft} \times \text{width}$ (width not given, assume same as triangle base) - Triangle area: $$\frac{1}{2} \times \text{base} \times 4.5\text{ ft}$$ - Since width/base is not given, assume width = base = unknown, so cannot calculate exact area without base. Since the base is missing for the flowerbed, we cannot compute the exact total area. **Final answers:** (i) $99\text{ mm}^2$ (ii) $24\text{ cm}^2$ (iii) $79\text{ in}^2$ (iv) $37.74\text{ yd}^2$ (v) Insufficient data to calculate total area of flowerbed.