The parallel sides of a trapezium field are 12 m and 20 m. If distance between the parallel sides is 8 m, find the area of the field.

Options

A. 128 sqm
B. 132 sq m
C. 130 sq m
D. 135 sq m

Answer

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

\[ \text{Area} = \frac{1}{2} \times (L_1 + L_2) \times h \]

where:
- \(L_1\) and \(L_2\) 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.**
- Given \(L_1 = 12 \, \text{m}\) and \(L_2 = 20 \, \text{m}\).
- The height \(h = 8 \, \text{m}\).

2. **Substitute the values into the area formula.**
\[ \text{Area} = \frac{1}{2} \times (12 + 20) \times 8 \]

3. **Calculate the sum of the parallel sides.**
\[ 12 + 20 = 32 \]

4. **Substitute the sum back into the area formula.**
\[ \text{Area} = \frac{1}{2} \times 32 \times 8 \]

5. **Calculate \(\frac{1}{2} \times 32\).**
\[ \frac{1}{2} \times 32 = 16 \]

6. **Now multiply by the height.**
\[ \text{Area} = 16 \times 8 \]

7. **Calculate \(16 \times 8\).**
\[ 16 \times 8 = 128 \]

8. **State the final answer.**
\[ \text{Area} = 128 \, \text{m}^2 \]

### Final Answer:
The area of the trapezium field is \(128 \, \text{m}^2\).