What is the area (in sq cm.) of a rhombus if the lengths of the diagonals are 12cm and 14cm?

Options

A. 42
B. 168
C. 84
D. 63

Answer

To find the area of a rhombus when the lengths of the diagonals are given, 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.

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Given \(d_1 = 12 \, \text{cm}\) (first diagonal)
- Given \(d_2 = 14 \, \text{cm}\) (second diagonal)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 12 \times 14 \]

3. **Calculate the product of the diagonals**:
- First, calculate \(12 \times 14\):
\[ 12 \times 14 = 168 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 168 = 84 \, \text{cm}^2 \]

5. **Final answer**:
- The area of the rhombus is \(84 \, \text{cm}^2\).