Here’s a step-by-step breakdown of solving the questions in your image:

Shape 1 (Parallelogram)

• Dimensions: Base = 6 cm, Height = 3 cm, Side length = 4 cm.

1. Perimeter: $\text{Perimeter} = 2 \times (\text{Base} + \text{Side length}) = 2 \times (6 + 4) = 20 \, \text{cm}.$
2. Area: $\text{Area} = \text{Base} \times \text{Height} = 6 \times 3 = 18 \, \text{cm}^2.$

Shape 2 (Trapezium)

• Dimensions: Parallel sides = 15 cm and 21 cm, Height = 4 cm, Non-parallel sides = 5 cm each.

1. Perimeter: $\text{Perimeter} = 15 + 21 + 5 + 5 = 46 \, \text{cm}.$
2. Area: $\text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times \text{Height} = \frac{1}{2} \times (15 + 21) \times 4 = 72 \, \text{cm}^2.$

Shape 3 (Rectangle)

• Dimensions: Length = 33 cm, Width = 22 cm.

1. Perimeter: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (33 + 22) = 110 \, \text{cm}.$
2. Area: $\text{Area} = \text{Length} \times \text{Width} = 33 \times 22 = 726 \, \text{cm}^2.$

Let me know if you’d like any part of this solution clarified further or if you have more questions!

Relative Questions:

1. How do you calculate the area of a triangle or other irregular shapes?
2. What is the difference between the formulas for the area of a parallelogram and a trapezium?
3. Why is perimeter measured in linear units while area is in square units?
4. Can the trapezium's area formula be used for parallelograms? Why or why not?
5. What are some real-life applications of calculating perimeter and area?

Tip:

Always label units (cm, cm², etc.) in your answers to avoid confusion and ensure clarity in calculations.