To calculate the total area of the trapezium and the parallelogram:

1. Area of the Trapezium (Yellow Shape):

The formula for the area of a trapezium is:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

• Base$_1$ = 21 cm (top)
• Base$_2$ = 16 cm (bottom)
• Height = 15 cm (vertical height)

$\text{Area}_{\text{trapezium}} = \frac{1}{2} \times (21 + 16) \times 15 = \frac{1}{2} \times 37 \times 15 = 277.5 \, \text{cm}^2$

2. Area of the Parallelogram (Pink Shape):

The formula for the area of a parallelogram is:

$\text{Area} = \text{Base} \times \text{Height}$

• Base = 16 cm
• Height = 7 cm

$\text{Area}_{\text{parallelogram}} = 16 \times 7 = 112 \, \text{cm}^2$

3. Total Area:

$\text{Total Area} = \text{Area}_{\text{trapezium}} + \text{Area}_{\text{parallelogram}} = 277.5 + 112 = 389.5 \, \text{cm}^2$

Final Answer:

The total area of the trapezium and the parallelogram is 389.5 cm².

Would you like a detailed breakdown of any step? Let me know!

Related Questions:

1. How is the height of the trapezium relevant to its area calculation?
2. Can the formula for the area of a parallelogram be derived from that of a rectangle?
3. What happens to the area calculation if the bases of the trapezium are swapped?
4. How can we verify the given dimensions are consistent for such diagrams?
5. Can you calculate the perimeter of the shapes if all side lengths are known?

Tip:

For any trapezium, always ensure the height is perpendicular to both bases before using it in the formula.