The area of a field in the shape of a hexagon is `3750 sqrt(3)m^(2)`. What will be the cost (in Rs) of putting fence around it at Rs 29 per metre?

Options

A. 1015
B. 7125
C. 9425
D. 8700

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Understand the area of a hexagon
The area \( A \) of a regular hexagon can be calculated using the formula:
\[ A = \frac{3\sqrt{3}}{2} s^2 \]
where \( s \) is the length of a side of the hexagon.

### Step 2: Set up the equation
Given that the area of the hexagon is \( 3750\sqrt{3} \) m², we can set up the equation:
\[ \frac{3\sqrt{3}}{2} s^2 = 3750\sqrt{3} \]

### Step 3: Simplify the equation
We can divide both sides of the equation by \( \sqrt{3} \):
\[ \frac{3}{2} s^2 = 3750 \]

### Step 4: Solve for \( s^2 \)
Next, we multiply both sides by \( \frac{2}{3} \) to isolate \( s^2 \):
\[ s^2 = 3750 \times \frac{2}{3} = 2500 \]

### Step 5: Find the length of the side \( s \)
Now, we take the square root of both sides to find \( s \):
\[ s = \sqrt{2500} = 50 \text{ m} \]

### Step 6: Calculate the perimeter of the hexagon
The perimeter \( P \) of a hexagon is given by:
\[ P = 6s \]
Substituting the value of \( s \):
\[ P = 6 \times 50 = 300 \text{ m} \]

### Step 7: Calculate the cost of fencing
The cost of fencing per meter is given as Rs 29. Therefore, the total cost \( C \) of fencing the hexagon is:
\[ C = 29 \times P = 29 \times 300 = 8700 \text{ Rs} \]

### Final Answer
The cost of putting a fence around the hexagon is Rs 8700.

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