What is the perpendicular distance (in cm) between the parallel sides of a trapezium whose area is 108 sq cm. and the length of the parallel sides are 9 cm and 36 cm?

Options

A. 3.6cm
B. 4.8cm
C. 7 m
D. 6 m

Answer

To find the perpendicular distance between the parallel sides of a trapezium, we can use the formula for the area of a trapezium. The formula is:

\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]

where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the perpendicular distance between the parallel sides.

Given:
- Area = 108 sq cm
- Length of the parallel sides \( a = 9 \) cm and \( b = 36 \) cm

We can substitute the values into the formula and solve for \( h \).

### Step-by-Step Solution:

1. **Write down the area formula for a trapezium:**
\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]

2. **Substitute the known values into the formula:**
\[ 108 = \frac{1}{2} \times (9 + 36) \times h \]

3. **Calculate the sum of the parallel sides:**
\[ 9 + 36 = 45 \]

4. **Substitute this sum back into the equation:**
\[ 108 = \frac{1}{2} \times 45 \times h \]

5. **Multiply both sides by 2 to eliminate the fraction:**
\[ 216 = 45 \times h \]

6. **Solve for \( h \) by dividing both sides by 45:**
\[ h = \frac{216}{45} \]

7. **Simplify the fraction:**
\[ h = \frac{216 \div 9}{45 \div 9} = \frac{24}{5} = 4.8 \]

8. **Conclusion:**
The perpendicular distance \( h \) between the parallel sides of the trapezium is \( 4.8 \) cm.

### Final Answer:
The perpendicular distance between the parallel sides of the trapezium is **4.8 cm**.