If parallel sides of a trapezium are 12 cm and 20 m respectively and distance between them 8 m, then area of trapezium would be

Options

A. 128 sq m
B. 130 sq m
C. 138 sq m
D. 140 sq m

Answer

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

\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]

where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the height (the distance between the parallel sides).

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the height**:
- Length of the first parallel side \( a = 12 \, \text{cm} \)
- Length of the second parallel side \( b = 20 \, \text{cm} \) (note: it should be converted to cm for consistency)
- Height \( h = 8 \, \text{m} = 800 \, \text{cm} \) (since 1 m = 100 cm)

2. **Calculate the sum of the parallel sides**:
\[ a + b = 12 \, \text{cm} + 20 \, \text{cm} = 32 \, \text{cm} \]

3. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times (32 \, \text{cm}) \times (800 \, \text{cm}) \]

4. **Calculate the area**:
- First, calculate \( \frac{1}{2} \times 32 = 16 \)
- Then, multiply by the height:
\[ \text{Area} = 16 \times 800 = 12800 \, \text{cm}^2 \]

5. **Convert the area back to square meters** (if needed):
\[ \text{Area} = 12800 \, \text{cm}^2 = 1.28 \, \text{m}^2 \]

### Final Answer:
The area of the trapezium is \( 12800 \, \text{cm}^2 \) or \( 1.28 \, \text{m}^2 \).