The area of a trapezium is 105 `meter^2` and the lengts 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, we will 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, and \(h\) is the height.

### Step-by-step solution:

1. **Identify the given values:**
- Area of the trapezium = 105 m²
- Length of the first parallel side \(a = 9\) m
- Length of the second parallel side \(b = 12\) m

2. **Substitute the values into 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 equation:**
\[ 105 = \frac{1}{2} \times 21 \times h \]

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

6. **Solve for \(h\) by dividing both sides by 21:**
\[ h = \frac{210}{21} = 10 \]

7. **Conclusion:**
The height of the trapezium is \(10\) meters.

### Final Answer:
The height of the trapezium is \(10\) meters.

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