Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm.

Answer

To find the area of a trapezium (also known as a trapezoid), we can use the formula:

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

where:
- \( a \) and \( b \) are the lengths of the two parallel sides,
- \( h \) is the distance (height) between the parallel sides.

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the height:**
- Let \( a = 24 \, \text{cm} \) (length of one parallel side)
- Let \( b = 20 \, \text{cm} \) (length of the other parallel side)
- Let \( h = 15 \, \text{cm} \) (distance between the parallel sides)

2. **Substitute the values into the area formula:**
\[ \text{Area} = \frac{1}{2} \times (24 + 20) \times 15 \]

3. **Calculate the sum of the parallel sides:**
\[ 24 + 20 = 44 \]

4. **Substitute the sum back into the formula:**
\[ \text{Area} = \frac{1}{2} \times 44 \times 15 \]

5. **Calculate the area:**
- First, calculate \( \frac{1}{2} \times 44 \):
\[ \frac{1}{2} \times 44 = 22 \]
- Now multiply by the height \( h \):
\[ 22 \times 15 = 330 \]

6. **Final result:**
\[ \text{Area} = 330 \, \text{cm}^2 \]

### Summary:
The area of the trapezium is \( 330 \, \text{cm}^2 \).