The area of a trapezium, whose parallel sides are 25 cm and 19 cm long. is 330 `cm^2`. The distance between the sides (in cm) is

Options

A. 10
B. 12
C. 30
D. 15

Answer

To find the distance between the parallel sides of the trapezium, 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 height (or the distance between the parallel sides).

Given:
- \( a = 25 \, \text{cm} \)
- \( b = 19 \, \text{cm} \)
- Area = \( 330 \, \text{cm}^2 \)

We need to find \( h \).

### Step 1: Substitute the values into the area formula.

\[ 330 = \frac{1}{2} \times (25 + 19) \times h \]

### Step 2: Calculate the sum of the parallel sides.

\[ 25 + 19 = 44 \]

### Step 3: Substitute the sum back into the equation.

\[ 330 = \frac{1}{2} \times 44 \times h \]

### Step 4: Simplify the equation.

\[ 330 = 22 \times h \]

### Step 5: Solve for \( h \).

\[ h = \frac{330}{22} \]

### Step 6: Perform the division.

\[ h = 15 \]

Thus, the distance between the parallel sides is \( 15 \, \text{cm} \).

### Final Answer:
The distance between the sides is \( 15 \, \text{cm} \).

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