If the lengths of the two parallel sides of a trapezium is 5 cm and 7 cm and its area is 24 `cm^2`. Find the distance between its parallel sides (in cm).

Options

A. 2
B. 4
C. 8
D. 6

Answer

To find the distance between the parallel sides of the trapezium, we can use 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,
- \( h \) is the height (or distance between the parallel sides).

Given:
- \( a = 5 \) cm,
- \( b = 7 \) cm,
- \( A = 24 \) cm².

We can substitute the known values into the area formula:

\[ 24 = \frac{1}{2} \times (5 + 7) \times h \]

Now, simplify the equation step by step:

1. Calculate \( (5 + 7) \):
\[ 5 + 7 = 12 \]

2. Substitute this back into the area equation:
\[ 24 = \frac{1}{2} \times 12 \times h \]

3. Multiply \( \frac{1}{2} \times 12 \):
\[ \frac{1}{2} \times 12 = 6 \]

4. Now the equation looks like:
\[ 24 = 6h \]

5. To find \( h \), divide both sides by 6:
\[ h = \frac{24}{6} \]

6. Calculate \( \frac{24}{6} \):
\[ h = 4 \]

Thus, the distance between the parallel sides of the trapezium is \( 4 \) cm.

### Summary of Steps:
1. Write the area formula for a trapezium.
2. Substitute the known values into the formula.
3. Simplify the equation step by step to isolate \( h \).
4. Calculate the final value of \( h \).