The parallel sides of a trapezium are 54 cm and 26 cm and the distance between them is 15 cm. The area of the trapezium is

Options

A. `702 cm^(2)`
B. `810 cm^(2)`
C. `405 cm^(2)`
D. `600 cm^(2)`

Answer

To find the area of the trapezium with given dimensions, 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 \( a = 54 \, \text{cm} \) and \( b = 26 \, \text{cm} \).

2. **Calculate the sum of the parallel sides:**
- Sum of the parallel sides \( = a + b = 54 \, \text{cm} + 26 \, \text{cm} = 80 \, \text{cm} \).

3. **Identify the distance between the parallel sides:**
- The distance (height) between the parallel sides \( h = 15 \, \text{cm} \).

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

5. **Substitute the values into the formula:**
- Substitute the sum of the parallel sides and the height into the formula:
\[ A = \frac{1}{2} \times 80 \, \text{cm} \times 15 \, \text{cm} \]

6. **Calculate the area:**
- First, calculate \( \frac{1}{2} \times 80 = 40 \).
- Then, multiply by the height:
\[ A = 40 \, \text{cm} \times 15 \, \text{cm} = 600 \, \text{cm}^2 \]

7. **State the final answer:**
- The area of the trapezium is \( 600 \, \text{cm}^2 \).