Parallel sides of a trapezium are 26 cm and 40 cm and the area is `792 cm^(2)`. What is the value of the distacne (in cm) between parallel sides ?

Options

A. 24
B. 48
C. 12
D. 36

Answer

To find the distance between the parallel sides of the trapezium, we will use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]

Where:
- \(\text{Base}_1 = 26 \, \text{cm}\)
- \(\text{Base}_2 = 40 \, \text{cm}\)
- \(\text{Area} = 792 \, \text{cm}^2\)
- \(\text{Height} = D\) (the distance between the parallel sides)

### Step 1: Set up the equation using the area formula
We can substitute the known values into the area formula:

\[ 792 = \frac{1}{2} \times (26 + 40) \times D \]

### Step 2: Simplify the equation
First, calculate the sum of the bases:

\[ 26 + 40 = 66 \]

Now substitute this back into the equation:

\[ 792 = \frac{1}{2} \times 66 \times D \]

### Step 3: Multiply both sides by 2 to eliminate the fraction
\[ 792 \times 2 = 66 \times D \]

This simplifies to:

\[ 1584 = 66D \]

### Step 4: Solve for D
Now, divide both sides by 66 to find D:

\[ D = \frac{1584}{66} \]

### Step 5: Calculate the value of D
Perform the division:

\[ D = 24 \]

Thus, the distance between the parallel sides of the trapezium is \(24 \, \text{cm}\).

### Final Answer:
The distance between the parallel sides is \(24 \, \text{cm}\).

---