Find the area of a rhombus in which
Q(i) each side = 2 dm and height = 12.6 cm.
(ii) 8 dm 5 cm and 5 dm 6 cm.

Answer

To solve the problem of finding the area of a rhombus for the two given cases, we will follow these steps:

### Part (i): Each side = 2 dm and height = 12.6 cm

1. **Convert the side length from decimeters to centimeters**:
- Given side length = 2 dm
- Conversion: 1 dm = 10 cm
- Therefore, \( 2 \, \text{dm} = 2 \times 10 = 20 \, \text{cm} \)

2. **Use the formula for the area of a rhombus**:
- The formula for the area of a rhombus is:
\[ \text{Area} = \text{Base} \times \text{Height} \]
- Here, the base (side length) is 20 cm and the height is 12.6 cm.

3. **Calculate the area**:
- Substitute the values into the formula:
\[ \text{Area} = 20 \, \text{cm} \times 12.6 \, \text{cm} \]
- Perform the multiplication:
\[ \text{Area} = 252 \, \text{cm}^2 \]

### Part (ii): Base = 8 dm 5 cm and height = 5 dm 6 cm

1. **Convert the base and height from mixed units to centimeters**:
- For the base:
- Given base = 8 dm 5 cm
- Conversion: \( 8 \, \text{dm} = 8 \times 10 = 80 \, \text{cm} \)
- Therefore, \( \text{Base} = 80 \, \text{cm} + 5 \, \text{cm} = 85 \, \text{cm} \)

- For the height:
- Given height = 5 dm 6 cm
- Conversion: \( 5 \, \text{dm} = 5 \times 10 = 50 \, \text{cm} \)
- Therefore, \( \text{Height} = 50 \, \text{cm} + 6 \, \text{cm} = 56 \, \text{cm} \)

2. **Use the formula for the area of a rhombus**:
- Substitute the values into the area formula:
\[ \text{Area} = \text{Base} \times \text{Height} = 85 \, \text{cm} \times 56 \, \text{cm} \]

3. **Calculate the area**:
- Perform the multiplication:
\[ \text{Area} = 4760 \, \text{cm}^2 \]

### Final Answers:
- Part (i): The area of the rhombus is \( 252 \, \text{cm}^2 \).
- Part (ii): The area of the rhombus is \( 4760 \, \text{cm}^2 \).