ABCD is trapezium in which `BC||AD` BC = 16 AD = 12 . Distance `b/w // `lines =10 cm find area

Answer

To find the area of trapezium ABCD where BC is parallel to AD, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides, and \( h \) is the height (the distance between the parallel sides).

### Step-by-step Solution:

1. **Identify the lengths of the parallel sides**:
- \( BC = 16 \) cm (this is \( b_1 \))
- \( AD = 12 \) cm (this is \( b_2 \))

2. **Identify the height (distance between the parallel sides)**:
- The distance between the parallel lines is given as \( h = 10 \) cm.

3. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
\[ \text{Area} = \frac{1}{2} \times (16 + 12) \times 10 \]

4. **Calculate \( b_1 + b_2 \)**:
\[ 16 + 12 = 28 \]

5. **Substitute back into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 28 \times 10 \]

6. **Calculate \( \frac{1}{2} \times 28 \)**:
\[ \frac{1}{2} \times 28 = 14 \]

7. **Now multiply by the height**:
\[ 14 \times 10 = 140 \]

8. **Final result**:
\[ \text{Area} = 140 \text{ cm}^2 \]

### Conclusion:
The area of trapezium ABCD is \( 140 \text{ cm}^2 \).