The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles, find the area of the quadrilateral.

Answer

To find the area of a quadrilateral whose diagonals intersect at right angles, 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 \( d_1 = 16 \) cm and \( d_2 = 13 \) cm.

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 16 \times 13 \]

3. **Calculate the product of the diagonals**:
\[ 16 \times 13 = 208 \]

4. **Divide the product by 2**:
\[ \text{Area} = \frac{208}{2} = 104 \text{ cm}^2 \]

5. **Conclusion**:
The area of the quadrilateral is \( 104 \text{ cm}^2 \).