To solve the problem, we will use the formula for the area of a trapezium (trapezoid), which is given by:

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

Here:

• The area of the trapezium is given as $516 \, \text{cm}^2$.
• The lengths of the two parallel sides (bases) are $\text{Base}_1 = 18 \, \text{cm}$ and $\text{Base}_2 = 24 \, \text{cm}$.

We are tasked with finding the height ($h$) between the two parallel lines.

Step 1: Substitute values into the formula

$516 = \frac{1}{2} \times (18 + 24) \times h$

Step 2: Simplify the equation

$516 = \frac{1}{2} \times 42 \times h$ $516 = 21 \times h$

Step 3: Solve for $h$

$h = \frac{516}{21}$ $h = 24.57 \, \text{cm} \, \approx \, 24.6 \, \text{cm}$

Final Answer:

The approximate distance between the two parallel lines is 24.6 cm. Therefore, the correct option is:

B. 24.6 cm

Would you like further explanation on any step? Here are some related questions:

1. What is the significance of the formula for the area of a trapezium?
2. How can you derive the formula for the area of a trapezium?
3. What other methods could be used to find the height in such problems?
4. How does the height of a trapezium impact its area calculation?
5. Could this problem be solved graphically or geometrically?

Tip: Always double-check units and verify if the approximations align with the question's requirements.