To calculate the area of the trapezium in the given problem, we use the formula for the area of a trapezium:

$\text{Area} = \frac{1}{2} \times (a + b) \times h$

where:

• $a$ and $b$ are the lengths of the parallel sides.
• $h$ is the height of the trapezium.

Step-by-Step Solution:

1. Identify the lengths of the parallel sides:

   • The top parallel side is $5 \, \text{cm}$.
   • The bottom parallel side is the sum of the segments $2 \, \text{cm}$ and $9 \, \text{cm} + 6 \, \text{cm}$: $a = 2 \, \text{cm} + 9 \, \text{cm} + 6 \, \text{cm} = 17 \, \text{cm}$

2. Identify the height ($h$):

   • The height between the parallel sides is $4 \, \text{cm}$.

3. Plug the values into the formula: $\text{Area} = \frac{1}{2} \times (5 + 17) \times 4$

4. Simplify the calculation: $\text{Area} = \frac{1}{2} \times 22 \times 4 = 11 \times 4 = 44 \, \text{cm}^2$

Final Answer:

The area of the given shape is 44 cm².

Would you like a more detailed explanation or have any questions?

Here are 5 related questions that may help deepen your understanding:

1. What is the formula for finding the area of a parallelogram?
2. How would you calculate the area of a triangle with given base and height?
3. What changes in the area formula if the height is not perpendicular in a trapezium?
4. How do the properties of a trapezium differ from those of a rectangle?
5. How can you use the area of a trapezium formula to solve problems in real-life scenarios?

Tip: When working with trapeziums, always ensure you correctly identify the lengths of the parallel sides and the height to apply the formula accurately.