Find the distance between the two parallel sides of a trapezium if the area of the trapezium is 500 sq m and the two parallel sides are equal to 30 m and 20 m, respectively.

Options

A. 20 cm
B. 15 cm
C. 18 cm
D. 25 cm

Answer

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

### Step 1: Understand 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 two parallel sides, and \( h \) is the height (the distance between the two parallel sides).

### Step 2: Identify the given values
From the problem, we have:
- Area \( A = 500 \, \text{m}^2 \)
- Length of the first parallel side \( a = 30 \, \text{m} \)
- Length of the second parallel side \( b = 20 \, \text{m} \)

### Step 3: Substitute the values into the area formula
We can substitute the known values into the area formula:
\[ 500 = \frac{1}{2} \times (30 + 20) \times h \]

### Step 4: Simplify the equation
First, calculate the sum of the parallel sides:
\[ 30 + 20 = 50 \]
Now substitute this back into the equation:
\[ 500 = \frac{1}{2} \times 50 \times h \]

### Step 5: Multiply both sides by 2 to eliminate the fraction
\[ 1000 = 50 \times h \]

### Step 6: Solve for \( h \)
Now, divide both sides by 50:
\[ h = \frac{1000}{50} = 20 \]

### Conclusion
The distance between the two parallel sides of the trapezium is \( 20 \, \text{m} \).

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