Let's go through each shape in the image to calculate their areas, rounding to 2 decimal places where necessary:

(a) L-shaped Figure

This can be broken into two rectangles.

1. Top rectangle:

   • Length = 52 mm
   • Height = 21 mm
   • Area = $52 \times 21 = 1092 \, \text{mm}^2$

2. Bottom rectangle:

   • Length = 19 mm
   • Height = 30 mm
   • Area = $19 \times 30 = 570 \, \text{mm}^2$

   Total Area for shape (a):
   $1092 + 570 = 1662 \, \text{mm}^2$.

(b) Triangular and Rectangular Combined Figure

This consists of a triangle and a rectangle.

1. Rectangle:

   • Length = 12 mm
   • Height = 10 mm
   • Area = $12 \times 10 = 120 \, \text{mm}^2$

2. Triangle:

   • Base = 12 mm
   • Height = 20 mm
   • Area = $\frac{1}{2} \times 12 \times 20 = 120 \, \text{mm}^2$

   Total Area for shape (b):
   $120 + 120 = 240 \, \text{mm}^2$.

(c) Composite Trapezoidal and Rectangular Shape

This consists of a trapezoid and a rectangle.

1. Rectangle:

   • Length = 12 cm
   • Height = 11 cm
   • Area = $12 \times 11 = 132 \, \text{cm}^2$

2. Trapezoid:

   • Height = 23 cm
   • Base 1 = 35 cm
   • Base 2 = 25 cm (since 35 cm - 10 cm = 25 cm)
   • Area = $\frac{1}{2} \times (35 + 25) \times 23 = 690 \, \text{cm}^2$

   Total Area for shape (c):
   $132 + 690 = 822 \, \text{cm}^2$.

(d) Combined Triangle and Trapezoid

1. Trapezoid:

   • Height = 7 cm
   • Base 1 = 15 cm
   • Base 2 = 4 cm
   • Area = $\frac{1}{2} \times (15 + 4) \times 7 = 66.5 \, \text{cm}^2$

2. Triangle:

   • Base = 6 cm
   • Height = 18 cm
   • Area = $\frac{1}{2} \times 6 \times 18 = 54 \, \text{cm}^2$

   Total Area for shape (d):
   $66.5 + 54 = 120.5 \, \text{cm}^2$.

Let me know if you need further details or clarification!

Related Questions:

1. How do you calculate the area of a triangle if the base and height are given in different units?
2. What is the formula for the area of a trapezoid?
3. How would you approach the problem if the shapes were in three dimensions (e.g., volume)?
4. Why is it important to convert all units to the same system before calculating the area?
5. Can you calculate the perimeter of any of these shapes based on the given information?

Tip:

When dealing with composite shapes, break them down into simpler geometric figures, calculate their areas individually, and then sum them.