The side of a rhombus is 26 meters and length of one of its diagonals is 20 metres . The area of the rhombus is

Options

A. `520 m^(2)`
B. `480 m^(2)`
C. ` 260 m^(2)`
D. `300 m^(2)`

Answer

To find the area of the rhombus given the side length and the length of one diagonal, we can follow these steps:

### Step 1: Identify the given values
- Side of the rhombus (a) = 26 meters
- Length of one diagonal (p) = 20 meters

### Step 2: Use the formula for the area of a rhombus
The area (A) of a rhombus can be calculated using the formula:
\[ A = \frac{1}{2} \times p \times \sqrt{4a^2 - p^2} \]
Where:
- \( p \) is the length of one diagonal
- \( a \) is the length of the side of the rhombus

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = \frac{1}{2} \times 20 \times \sqrt{4 \times (26)^2 - (20)^2} \]

### Step 4: Calculate \( 4a^2 \) and \( p^2 \)
First, calculate \( 4a^2 \):
\[ 4a^2 = 4 \times (26)^2 = 4 \times 676 = 2704 \]
Now, calculate \( p^2 \):
\[ p^2 = (20)^2 = 400 \]

### Step 5: Calculate \( 4a^2 - p^2 \)
Now, subtract \( p^2 \) from \( 4a^2 \):
\[ 4a^2 - p^2 = 2704 - 400 = 2304 \]

### Step 6: Calculate the square root
Now, find the square root of \( 2304 \):
\[ \sqrt{2304} = 48 \]

### Step 7: Substitute back into the area formula
Now substitute back into the area formula:
\[ A = \frac{1}{2} \times 20 \times 48 \]

### Step 8: Calculate the area
Now calculate the area:
\[ A = 10 \times 48 = 480 \text{ square meters} \]

### Final Answer
The area of the rhombus is \( 480 \) square meters.

---