The two parallel sides of a trapezium are 27 cm and 13 cm respectively. If the height of the trapezium is 8 cm, then what is its area in `m^2` ?

Options

A. 0.016
B. 0.032
C. 0.056
D. 0.32

Answer

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

**Area = (1/2) × (a + b) × h**

where:
- a and b are the lengths of the two parallel sides,
- h is the height of the trapezium.

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the height**:
- a = 27 cm (length of the first parallel side)
- b = 13 cm (length of the second parallel side)
- h = 8 cm (height of the trapezium)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times (27 + 13) \times 8 \]

3. **Calculate the sum of the parallel sides**:
\[ 27 + 13 = 40 \]

4. **Substitute the sum back into the formula**:
\[ \text{Area} = \frac{1}{2} \times 40 \times 8 \]

5. **Calculate the area**:
\[ \text{Area} = \frac{1}{2} \times 40 \times 8 = 20 \times 8 = 160 \text{ cm}^2 \]

6. **Convert the area from cm² to m²**:
Since 1 m² = 10,000 cm², we convert the area:
\[ \text{Area in m}^2 = \frac{160 \text{ cm}^2}{10000} = 0.016 \text{ m}^2 \]

### Final Answer:
The area of the trapezium is **0.016 m²**.