The length of the parallel sides of a trapezium are 14 cm and 7 cm. If the perpendicular distance between them is 8 cm, then the area of the trapezium is:

Options

A. 86
B. 84
C. 64
D. 76

Answer

To find the area of the trapezium with parallel sides of lengths 14 cm and 7 cm, and a perpendicular distance (height) of 8 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides**:
- Let the lengths of the parallel sides be \( a = 14 \, \text{cm} \) and \( b = 7 \, \text{cm} \).

2. **Identify the height of the trapezium**:
- The height \( h \) (perpendicular distance between the parallel sides) is given as \( h = 8 \, \text{cm} \).

3. **Use the formula for the area of a trapezium**:
- The formula for the area \( A \) of a trapezium is:
\[ A = \frac{1}{2} \times (a + b) \times h \]

4. **Substitute the values into the formula**:
- Substitute \( a = 14 \, \text{cm} \), \( b = 7 \, \text{cm} \), and \( h = 8 \, \text{cm} \):
\[ A = \frac{1}{2} \times (14 + 7) \times 8 \]

5. **Calculate the sum of the parallel sides**:
- Calculate \( a + b = 14 + 7 = 21 \, \text{cm} \).

6. **Calculate the area**:
- Now substitute back into the area formula:
\[ A = \frac{1}{2} \times 21 \times 8 \]
- Simplify:
\[ A = \frac{21 \times 8}{2} = \frac{168}{2} = 84 \, \text{cm}^2 \]

7. **Conclusion**:
- Therefore, the area of the trapezium is \( 84 \, \text{cm}^2 \).