The perimeter of a rhombus is 46 cm. If the height of rhombus is 8 cm, find its area.

Answer

To find the area of the rhombus given its perimeter and height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given information:**
- Perimeter of the rhombus = 46 cm
- Height of the rhombus = 8 cm

2. **Use the formula for the perimeter of a rhombus:**
The perimeter \( P \) of a rhombus is given by the formula:
\[ P = 4s \]
where \( s \) is the length of one side.

3. **Calculate the length of one side:**
Rearranging the formula for the perimeter, we can find \( s \):
\[ s = \frac{P}{4} = \frac{46}{4} = 11.5 \text{ cm} \]

4. **Use the formula for the area of a rhombus:**
The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
In this case, the base is the length of one side \( s \) and the height is given.

5. **Substitute the values into the area formula:**
\[ A = s \times \text{height} = 11.5 \times 8 \]

6. **Calculate the area:**
\[ A = 11.5 \times 8 = 92 \text{ cm}^2 \]

### Final Answer:
The area of the rhombus is \( 92 \text{ cm}^2 \).

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