The area of a trapezium is `880 cm^(2)`. The lengths of the parallel sides are 60 cm and 28 cm respectively. Find the distance between the parallel sides.

Answer

To find the distance between the parallel sides of a trapezium given its area and the lengths of the parallel sides, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the formula for the area of a trapezium:**
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
where \( a \) and \( b \) are the lengths of the parallel sides, and \( h \) is the distance between them.

2. **Identify the given values:**
From the problem, we have:
- Area \( A = 880 \, \text{cm}^2 \)
- Length of the first parallel side \( a = 60 \, \text{cm} \)
- Length of the second parallel side \( b = 28 \, \text{cm} \)

3. **Substitute the known values into the formula:**
We can substitute the values into the area formula:
\[ 880 = \frac{1}{2} \times (60 + 28) \times h \]

4. **Calculate the sum of the parallel sides:**
First, calculate \( 60 + 28 \):
\[ 60 + 28 = 88 \]
Now substitute this back into the equation:
\[ 880 = \frac{1}{2} \times 88 \times h \]

5. **Simplify the equation:**
Multiply both sides by 2 to eliminate the fraction:
\[ 1760 = 88 \times h \]

6. **Solve for \( h \):**
Now, divide both sides by 88 to find \( h \):
\[ h = \frac{1760}{88} \]
Calculating this gives:
\[ h = 20 \, \text{cm} \]

### Final Answer:
The distance between the parallel sides of the trapezium is \( 20 \, \text{cm} \).

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