The parallel sides of a trapezium are 30 cm and 20 cm and the area of it is `450cm^(2)`, the distance between the parallel sides is

Options

A. 16 cm
B. 18 cm
C. 19 cm
D. 20 cm

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,
- \( h \) is the distance between the parallel sides (height).

### Step-by-step Solution:

1. **Identify the lengths of the parallel sides**:
- Let \( a = 30 \, \text{cm} \) (longer side)
- Let \( b = 20 \, \text{cm} \) (shorter side)

2. **Identify the area of the trapezium**:
- Given area \( = 450 \, \text{cm}^2 \)

3. **Substitute the values into the area formula**:
\[ 450 = \frac{1}{2} \times (30 + 20) \times h \]

4. **Calculate the sum of the parallel sides**:
\[ 30 + 20 = 50 \]

5. **Substitute the sum back into the equation**:
\[ 450 = \frac{1}{2} \times 50 \times h \]

6. **Simplify the equation**:
\[ 450 = 25h \]

7. **Solve for \( h \)**:
\[ h = \frac{450}{25} \]
\[ h = 18 \, \text{cm} \]

### Final Answer:
The distance between the parallel sides of the trapezium is \( 18 \, \text{cm} \).