In a trapezium ABCD, AB || CD, `AB lt CD, CD = 6 cm` and distance between the parallel sides is 4 cm. If the area of ABCD is `16 cm^(2)`, then AB is

Options

A. 1 cm
B. 2 cm
C. 3 cm
D. 8 cm

Answer

To find the length of side AB in trapezium ABCD, where AB is parallel to CD, we can use the formula for the area of a trapezium.

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of CD = 6 cm
- Distance between the parallel sides (height) = 4 cm
- Area of trapezium ABCD = 16 cm²

2. **Use the area formula for a trapezium:**
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (AB + CD) \times \text{height} \]
Substituting the known values into the formula:
\[ 16 = \frac{1}{2} \times (AB + 6) \times 4 \]

3. **Simplify the equation:**
Multiply both sides by 2 to eliminate the fraction:
\[ 32 = (AB + 6) \times 4 \]
Now, divide both sides by 4:
\[ 8 = AB + 6 \]

4. **Solve for AB:**
Subtract 6 from both sides:
\[ AB = 8 - 6 \]
\[ AB = 2 \text{ cm} \]

### Conclusion:
The length of AB is **2 cm**.