If the side of a rhombus is 10 cm and one diagonal is 16 cm, then area of the rhombus is 96 `cm^(2)`.

Explanation

To find the area of the rhombus given that one side is 10 cm and one diagonal is 16 cm, we can follow these steps:

### Step 1: Understand the properties of the rhombus
A rhombus has all sides equal, and its diagonals bisect each other at right angles.

### Step 2: Identify the given information
- Side of the rhombus (AB) = 10 cm
- One diagonal (AC) = 16 cm

### Step 3: Find half of the diagonal
Since the diagonals bisect each other, we can find half of diagonal AC:
\[ AO = \frac{AC}{2} = \frac{16}{2} = 8 \text{ cm} \]

### Step 4: Use the Pythagorean theorem
In triangle AOB, we can apply the Pythagorean theorem:
\[ AB^2 = AO^2 + OB^2 \]
Where:
- \( AB = 10 \text{ cm} \)
- \( AO = 8 \text{ cm} \)
- \( OB \) is the unknown we need to find.

Substituting the known values:
\[ 10^2 = 8^2 + OB^2 \]
\[ 100 = 64 + OB^2 \]

### Step 5: Solve for OB
Rearranging the equation to find \( OB^2 \):
\[ OB^2 = 100 - 64 = 36 \]
Taking the square root:
\[ OB = \sqrt{36} = 6 \text{ cm} \]

### Step 6: Find the second diagonal
Since OB is half of diagonal BD, we can find BD:
\[ BD = 2 \times OB = 2 \times 6 = 12 \text{ cm} \]

### Step 7: Calculate the area of the rhombus
The formula for the area of a rhombus is:
\[ \text{Area} = \frac{1}{2} \times (d_1 \times d_2) \]
Where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.
Substituting the values we have:
\[ \text{Area} = \frac{1}{2} \times (16 \times 12) \]
\[ \text{Area} = \frac{1}{2} \times 192 = 96 \text{ cm}^2 \]

### Conclusion
Thus, the area of the rhombus is \( 96 \text{ cm}^2 \), confirming that the statement is true.

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