If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm. and its area is `54 cm^(2)`. Find the distance between its parallel sides (in cm.).

Options

A. 6
B. 3
C. 12
D. 9

Answer

To find the distance between the parallel sides of a trapezium given the lengths of the parallel sides and the area, we can 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, and \(h\) is the distance between them.

### Step-by-step Solution:

1. **Identify the given values:**
- Length of the first parallel side, \(a = 8 \, \text{cm}\)
- Length of the second parallel side, \(b = 10 \, \text{cm}\)
- Area of the trapezium, \(A = 54 \, \text{cm}^2\)

2. **Write the area formula:**
\[ A = \frac{1}{2} \times (a + b) \times h \]

3. **Substitute the known values into the formula:**
\[ 54 = \frac{1}{2} \times (8 + 10) \times h \]

4. **Calculate the sum of the parallel sides:**
\[ 8 + 10 = 18 \]
So the equation becomes:
\[ 54 = \frac{1}{2} \times 18 \times h \]

5. **Multiply both sides by 2 to eliminate the fraction:**
\[ 2 \times 54 = 18 \times h \]
\[ 108 = 18h \]

6. **Solve for \(h\):**
\[ h = \frac{108}{18} \]
\[ h = 6 \]

7. **Conclusion:**
The distance between the parallel sides of the trapezium is \(6 \, \text{cm}\).