To find the area of the trapezium, we can use the trapezium area formula:

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

From the image:

• The two parallel sides (bases) are $3 \, \text{cm}$ and $9 \, \text{cm}$.
• The height, which is perpendicular to these bases, is $4 \, \text{cm}$.

Step-by-Step Calculation:

1. Add the lengths of the two bases: $3 + 9 = 12 \, \text{cm}$

2. Multiply by the height and divide by 2: $\text{Area} = \frac{1}{2} \times 12 \times 4$

3. Calculate the area: $\text{Area} = \frac{1}{2} \times 48 = 24 \, \text{cm}^2$

Final Answer:

The area of the trapezium is $24 \, \text{cm}^2$.

Would you like a detailed breakdown of each calculation step?

Here are 5 related questions to deepen your understanding:

1. How does the height of a trapezium affect its area?
2. What if both bases were equal in length? How would that impact the area?
3. Can you calculate the area if the height is unknown but both sides and angles are given?
4. How does the area formula for a trapezium relate to that of a parallelogram?
5. What happens to the area if the bases are doubled but the height remains the same?

Tip: Always ensure the height is perpendicular to the bases when using the trapezium area formula.