Find the area of rhombus whose diagonals are :
(i) 12 cm , 21 cm
(ii) 17.8 cm , 25 cm

Answer

To find the area of a rhombus using its diagonals, we can use the formula:

\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]

where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Part (i): Diagonals of 12 cm and 21 cm

1. **Identify the diagonals**:
- \(d_1 = 12 \, \text{cm}\)
- \(d_2 = 21 \, \text{cm}\)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 12 \times 21 \]

3. **Calculate the product of the diagonals**:
\[ 12 \times 21 = 252 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 252 = 126 \, \text{cm}^2 \]

### Part (ii): Diagonals of 17.8 cm and 25 cm

1. **Identify the diagonals**:
- \(d_1 = 17.8 \, \text{cm}\)
- \(d_2 = 25 \, \text{cm}\)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 17.8 \times 25 \]

3. **Calculate the product of the diagonals**:
\[ 17.8 \times 25 = 445 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 445 = 222.5 \, \text{cm}^2 \]

### Final Answers:
- For part (i), the area of the rhombus is \(126 \, \text{cm}^2\).
- For part (ii), the area of the rhombus is \(222.5 \, \text{cm}^2\).