Let's break this down step by step and calculate the areas for each composite shape.

Shape (i)

This shape consists of:

1. A rectangle: $8 \, \text{cm} \times 11 \, \text{cm}$
2. A right triangle with:
   • Base: $8 \, \text{cm}$
   • Height: $6 \, \text{cm}$

Area of the rectangle: $\text{Area} = \text{length} \times \text{width} = 8 \times 11 = 88 \, \text{cm}^2$

Area of the triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2$

Total area of shape (i): $88 + 24 = 112 \, \text{cm}^2$

Shape (ii)

This shape consists of:

1. A rectangle: $14 \, \text{cm} \times 10 \, \text{cm}$
2. A right triangle with:
   • Base: $14 \, \text{cm}$
   • Height: $16 - 10 = 6 \, \text{cm}$

Area of the rectangle: $\text{Area} = \text{length} \times \text{width} = 14 \times 10 = 140 \, \text{cm}^2$

Area of the triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 14 \times 6 = 42 \, \text{cm}^2$

Total area of shape (ii): $140 + 42 = 182 \, \text{cm}^2$

Shape (iii)

This shape consists of:

1. A rectangle: $20 \, \text{cm} \times 15 \, \text{cm}$
2. A right triangle with:
   • Base: $20 - 12 = 8 \, \text{cm}$
   • Height: $12 \, \text{cm}$

Area of the rectangle: $\text{Area} = \text{length} \times \text{width} = 20 \times 15 = 300 \, \text{cm}^2$

Area of the triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 12 = 48 \, \text{cm}^2$

Total area of shape (iii): $300 + 48 = 348 \, \text{cm}^2$

Final Results:

1. Area of shape (i): $112 \, \text{cm}^2$
2. Area of shape (ii): $182 \, \text{cm}^2$
3. Area of shape (iii): $348 \, \text{cm}^2$

Would you like any step explained further or have another question?

Expansion Questions:

1. Can you confirm why the base and height are used for triangles?
2. Would you like more practice problems for composite shapes?
3. How do the Pythagorean theorem or other triangle properties help here?
4. Should I explain the relation between rectangles and parallelograms?
5. Do you want a method to visualize composite shapes more effectively?

Tip:

When calculating areas for composite shapes, always break them into simpler components like rectangles, triangles, or circles.