In a trapezium , the sum of the lengths of the parallel sides is 32 cm and the area of the trapezium is 128 sq. cm . Calculate the distance between the parallel sides .

Options

A. 7 cm
B. 8 cm
C. 10 cm
D. 12 cm

Answer

To solve the problem, we need to find the distance between the parallel sides of a trapezium given the sum of the lengths of the parallel sides and the area of the trapezium.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The sum of the lengths of the parallel sides (AB + CD) = 32 cm
- The area of the trapezium = 128 sq. cm

2. **Use the Area Formula for a Trapezium:**
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (AB + CD) \times h \]
where \( h \) is the distance between the parallel sides.

3. **Substitute the Known Values into the Formula:**
Here, we know that \( AB + CD = 32 \) cm and \( A = 128 \) sq. cm. We can substitute these values into the area formula:
\[ 128 = \frac{1}{2} \times 32 \times h \]

4. **Simplify the Equation:**
First, calculate \( \frac{1}{2} \times 32 \):
\[ \frac{1}{2} \times 32 = 16 \]
Now, substitute this back into the equation:
\[ 128 = 16 \times h \]

5. **Solve for \( h \):**
To find \( h \), divide both sides of the equation by 16:
\[ h = \frac{128}{16} \]
Calculate the right-hand side:
\[ h = 8 \text{ cm} \]

6. **Conclusion:**
The distance between the parallel sides of the trapezium is \( 8 \) cm.

### Final Answer:
The distance between the parallel sides is **8 cm**.