The area of a trapezium is 105 sq. m and the lengths of its parallel sides are 9 m and 12 m respectively then the height of the trapezium is :

Options

A. 15 m
B. 12 m
C. 5 m
D. 10 m

Answer

To find the height of the trapezium given its area and the lengths of its parallel sides, 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 of the trapezium.

### Step-by-Step Solution:

1. **Identify the given values:**
- Area \( = 105 \, \text{sq. m} \)
- Length of parallel side \( a = 9 \, \text{m} \)
- Length of parallel side \( b = 12 \, \text{m} \)

2. **Write the area formula:**
\[ 105 = \frac{1}{2} \times (9 + 12) \times h \]

3. **Calculate the sum of the parallel sides:**
\[ 9 + 12 = 21 \]

4. **Substitute the sum back into the area formula:**
\[ 105 = \frac{1}{2} \times 21 \times h \]

5. **Multiply both sides by 2 to eliminate the fraction:**
\[ 210 = 21 \times h \]

6. **Solve for \( h \) by dividing both sides by 21:**
\[ h = \frac{210}{21} \]

7. **Calculate the height:**
\[ h = 10 \, \text{m} \]

### Final Answer:
The height of the trapezium is \( 10 \, \text{m} \).

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