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To calculate the area of the trapezium \( CDEF \), we can use the following steps based on the provided diagram and given information:

### Step 1: Understand the Geometry
- \( CDEF \) is a trapezium.
- \( ABCF \) is a rectangle with a height \( AB = 6 \, \text{cm} \) and length \( BD = 10 \, \text{cm} \).
- \( EF = 2 \, \text{cm} \), and the perimeter of \( ABCF \) is \( 26 \, \text{cm} \).
  
### Step 2: Identify the Sides of the Trapezium
In a trapezium, the area is calculated by the formula:
\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\]
Where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the height (the perpendicular distance between the parallel sides).

From the diagram:
- One parallel side is \( CD = 10 \, \text{cm} \) (length of the rectangle's top side).
- The other parallel side is \( EF = 2 \, \text{cm} \).

### Step 3: Find the Height of the Trapezium
The height of the trapezium is the same as the height of the rectangle \( ABCF \), which is \( AB = 6 \, \text{cm} \).

### Step 4: Apply the Formula
Now we can calculate the area of the trapezium:
\[
\text{Area} = \frac{1}{2} \times (CD + EF) \times AB
\]
Substituting the known values:
\[
\text{Area} = \frac{1}{2} \times (10 + 2) \times 6 = \frac{1}{2} \times 12 \times 6 = 36 \, \text{cm}^2
\]

Thus, the area of the trapezium \( CDEF \) is **36 cm²**.

Would you like further details or clarifications?

Here are 5 related questions to expand on this:

1. How would you calculate the perimeter of the trapezium \( CDEF \)?
2. Can the Pythagorean theorem be used in this problem? If so, where?
3. What other methods can be used to find the area of irregular quadrilaterals?
4. How would the area change if the length of \( EF \) was different?
5. What is the significance of knowing the perimeter of \( ABCF \) in this problem?

**Tip:** Always ensure to double-check units in geometry problems to avoid miscalculations in areas or perimeters.

In the diagram shown, CDEF is a trapezium, ABCF is a rectangle, BD = 10 cm, AB = 6 cm, EF = 2 cm, Perimeter of ABCF = 26 cm. Calculate the area of trapezium CDEF.

Learn how to calculate the area of trapezium CDEF using the area formula for trapeziums. This geometry problem involves basic concepts such as parallel sides, height, and applying the area formula for trapeziums. Suitable for students in Grades 6-8.

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