If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm and the distance between these parallel sides is 6 cm. Find its area (in `cm^(2)`).

Options

A. 27
B. 108
C. 54
D. 81

Answer

To find the area of the trapezium, we can use the formula for the area of a trapezium:

**Area = (1/2) × (Sum of the lengths of the parallel sides) × (Distance between the parallel sides)**

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the distance between them:**
- Length of the first parallel side (a) = 8 cm
- Length of the second parallel side (b) = 10 cm
- Distance between the parallel sides (h) = 6 cm

2. **Calculate the sum of the lengths of the parallel sides:**
- Sum of parallel sides = a + b = 8 cm + 10 cm = 18 cm

3. **Substitute the values into the area formula:**
- Area = (1/2) × (Sum of parallel sides) × (Distance between the parallel sides)
- Area = (1/2) × 18 cm × 6 cm

4. **Calculate the area:**
- Area = (1/2) × 18 × 6
- Area = 9 × 6
- Area = 54 cm²

### Final Answer:
The area of the trapezium is **54 cm²**.

---