ABCD is a trapezium with AB || CD. If AB = 10 cm, CD = 7 cm and area of trapezium = 102 `"cm"^(2)`, then find the height of trapezium (in cm).

Options

A. A)10
B. B)12
C. C)14
D. D)16

Answer

To find the height of trapezium ABCD with given dimensions, we can use the formula for the area of a trapezium. The area \( A \) of a trapezium can be calculated using the formula:

\[ A = \frac{(AB + CD)}{2} \times h \]

where \( AB \) and \( CD \) are the lengths of the parallel sides, and \( h \) is the height of the trapezium.

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides:**
- Given \( AB = 10 \, \text{cm} \)
- Given \( CD = 7 \, \text{cm} \)

2. **Calculate the sum of the lengths of the parallel sides:**
\[ AB + CD = 10 + 7 = 17 \, \text{cm} \]

3. **Use the area of the trapezium:**
- Given area \( A = 102 \, \text{cm}^2 \)

4. **Substitute the values into the area formula:**
\[ 102 = \frac{(AB + CD)}{2} \times h \]
\[ 102 = \frac{17}{2} \times h \]

5. **Multiply both sides by 2 to eliminate the fraction:**
\[ 204 = 17h \]

6. **Solve for \( h \):**
\[ h = \frac{204}{17} \]
\[ h = 12 \, \text{cm} \]

### Final Answer:
The height of the trapezium is \( h = 12 \, \text{cm} \).