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

Options

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

Answer

To find the area of the trapezium field with parallel sides of lengths 12 m and 20 m, and a distance (height) of 8 m between the parallel sides, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the height**:
- Let the lengths of the parallel sides be \( A = 12 \, \text{m} \) and \( B = 20 \, \text{m} \).
- The height (distance between the parallel sides) is \( h = 8 \, \text{m} \).

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

3. **Substitute the values into the formula**:
- Substitute \( A = 12 \, \text{m} \), \( B = 20 \, \text{m} \), and \( h = 8 \, \text{m} \) into the formula:
\[ \text{Area} = \frac{1}{2} \times (12 + 20) \times 8 \]

4. **Calculate the sum of the parallel sides**:
- Calculate \( 12 + 20 = 32 \).

5. **Continue with the area calculation**:
- Now substitute back into the area formula:
\[ \text{Area} = \frac{1}{2} \times 32 \times 8 \]

6. **Calculate half of 32**:
- Calculate \( \frac{32}{2} = 16 \).

7. **Multiply by the height**:
- Now multiply \( 16 \) by \( 8 \):
\[ \text{Area} = 16 \times 8 = 128 \, \text{m}^2 \]

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