The perimeter of a rhombus is 40 m and its height is 5 m. Its area is :

Options

A. `60 m^2`
B. `50 m^2`
C. `45 m^2`
D. `55 m^2`

Answer

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

### Step 1: Understand the properties of a rhombus
A rhombus is a type of quadrilateral where all four sides are of equal length. The perimeter of a rhombus is given by the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]

### Step 2: Use the perimeter to find the length of one side
We are given that the perimeter of the rhombus is 40 meters. We can set up the equation:
\[ 4 \times \text{side} = 40 \]
To find the length of one side, we divide both sides by 4:
\[ \text{side} = \frac{40}{4} = 10 \text{ meters} \]

### Step 3: Use the height to find the area
The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \text{side} \times \text{height} \]
We know the side is 10 meters and the height is given as 5 meters. Plugging in these values:
\[ A = 10 \text{ m} \times 5 \text{ m} = 50 \text{ m}^2 \]

### Conclusion
The area of the rhombus is \( 50 \text{ m}^2 \).

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