Let's solve this step by step.

We need to calculate the total area of the trapezium and the parallelogram shown in the image.

1. Area of the Trapezium

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

• $a = 21 \, \text{cm}$ (top base),
• $b = 14 \, \text{cm}$ (bottom base),
• $h = 11 \, \text{cm}$ (height).

Substitute the values: $\text{Area of trapezium} = \frac{1}{2} \times (21 + 14) \times 11$
$\text{Area of trapezium} = \frac{1}{2} \times 35 \times 11$
$\text{Area of trapezium} = 192.5 \, \text{cm}^2$

2. Area of the Parallelogram

The formula for the area of a parallelogram is:
$\text{Area} = \text{base} \times \text{height}$
Where:

• Base = $14 \, \text{cm}$,
• Height = $5 \, \text{cm}$.

Substitute the values: $\text{Area of parallelogram} = 14 \times 5$
$\text{Area of parallelogram} = 70 \, \text{cm}^2$

3. Total Area

Now, add the areas of the trapezium and parallelogram: $\text{Total area} = 192.5 + 70$
$\text{Total area} = 262.5 \, \text{cm}^2$

Final Answer

The total area of the trapezium and the parallelogram is:
$\boxed{262.5 \, \text{cm}^2}$

Do you need further clarification or step-by-step explanation on any part?

Here are 5 related questions for practice:

1. What is the area of a trapezium with bases $18 \, \text{cm}$ and $12 \, \text{cm}$ and height $10 \, \text{cm}$?
2. Calculate the area of a parallelogram with base $20 \, \text{cm}$ and height $8 \, \text{cm}$.
3. If the height of the trapezium is doubled, how does the area change?
4. How would you calculate the perimeter of the parallelogram in the given image?
5. What happens to the total area if the base of the parallelogram increases by $2 \, \text{cm}$?

Tip: Always double-check the height and base measurements when working with trapeziums and parallelograms!