Let's go through the shapes and find their areas one by one.

Shape (c) – L-shaped figure:

This figure is an L-shape made of two rectangles. We can divide it into two smaller rectangles:

• Bottom rectangle:

  • Width = 6 m
  • Height = 2 m
  • Area = $6 \times 2 = 12 \, \text{m}^2$

• Upper rectangle:

  • Width = 5 m
  • Height = 2 m
  • Area = $5 \times 2 = 10 \, \text{m}^2$

The total area is the sum of the two areas: $\text{Total Area} = 12 + 10 = 22 \, \text{m}^2$

Shape (d) – Trapezium:

For a trapezium, the formula for the area is: $\text{Area} = \frac{1}{2} \times (a + b) \times h$ Where:

• $a = 8 \, \text{m}$ (top base)
• $b = 9 \, \text{m}$ (bottom base)
• $h = 4 \, \text{m}$ (height)

$\text{Area} = \frac{1}{2} \times (8 + 9) \times 4 = \frac{1}{2} \times 17 \times 4 = 34 \, \text{m}^2$

Shape (e) – Square with a triangle inside:

We will calculate the area of the square and subtract the area of the triangle.

• Square:

  • Side = 20 cm
  • Area = $20 \times 20 = 400 \, \text{cm}^2$

• Triangle:

  • Base = 14 cm
  • Height = 20 cm
  • Area = $\frac{1}{2} \times 14 \times 20 = 140 \, \text{cm}^2$

The area of the remaining part (after subtracting the triangle) is: $\text{Remaining Area} = 400 - 140 = 260 \, \text{cm}^2$

Shape (f) – Composite triangle and rectangle:

This figure has a triangle on top of a rectangle.

• Rectangle:

  • Width = 4 m
  • Height = 1 m
  • Area = $4 \times 1 = 4 \, \text{m}^2$

• Triangle:

  • Base = 4 m
  • Height = 2.5 m
  • Area = $\frac{1}{2} \times 4 \times 2.5 = 5 \, \text{m}^2$

The total area is: $\text{Total Area} = 4 + 5 = 9 \, \text{m}^2$

If you have any questions or want more details, feel free to ask!

Follow-up questions:

1. What is the total area of all the shapes combined?
2. Can you calculate the perimeter of shape (c)?
3. How would you modify the trapezium’s formula for different height values?
4. Can you explain how to find the area of irregular polygons?
5. What is the relation between the areas of a square and a triangle inside it?

Tip: When working with composite figures, always break them down into smaller, simpler shapes (like rectangles or triangles) for easier calculations.