Diagonals of a parallelogram are 8 m and 6 m respectively. If one of side is 5m, then the area of parallelogram is:

Options

A. `18 m^(2)`
B. `30 m^(2)`
C. `24 m^(2)`
D. `48 m^(2)`

Answer

To find the area of the parallelogram given the lengths of its diagonals and one side, we can use the formula that relates the diagonals of a parallelogram to its area. Here’s a step-by-step solution:

### Step 1: Identify the lengths of the diagonals
We are given:
- Diagonal 1 (d1) = 8 m
- Diagonal 2 (d2) = 6 m

### Step 2: Use the area formula for a parallelogram
The area (A) of a parallelogram can be calculated using the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]
Where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Step 3: Substitute the values into the formula
Substituting the values of the diagonals into the formula:
\[ A = \frac{1}{2} \times 8 \times 6 \]

### Step 4: Calculate the area
First, calculate \(8 \times 6\):
\[ 8 \times 6 = 48 \]
Now, divide by 2:
\[ A = \frac{48}{2} = 24 \text{ m}^2 \]

### Final Answer
The area of the parallelogram is:
\[ \text{Area} = 24 \text{ m}^2 \]

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