The diagonals of a field in the form of a quadrilateral are 106 m and 80 m and intersect each other at right angles. Find the cost of cultivating the field at the rate of 25.50 per 100 `m^(2)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the area of the quadrilateral
Given that the diagonals of the quadrilateral intersect at right angles, we can use the formula for the area of a quadrilateral with diagonals \(d_1\) and \(d_2\):
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]
Here, \(d_1 = 106 \, \text{m}\) and \(d_2 = 80 \, \text{m}\).

### Calculation:
\[ \text{Area} = \frac{1}{2} \times 106 \times 80 \]
\[ = \frac{1}{2} \times 8480 \]
\[ = 4240 \, \text{m}^2 \]

### Step 2: Calculate the cost of cultivating the field
The cost of cultivating is given as 25.50 rupees per 100 m². To find the total cost for the area of 4240 m², we can set up a proportion:
\[ \text{Cost} = \left(\frac{25.50}{100}\right) \times \text{Area} \]

### Calculation:
\[ \text{Cost} = \left(\frac{25.50}{100}\right) \times 4240 \]
\[ = 25.50 \times 42.4 \]
\[ = 1081.20 \, \text{rupees} \]

Thus, the total cost of cultivating the field is **1081.20 rupees**.

### Summary of Steps:
1. Calculate the area of the quadrilateral using the formula for the area with diagonals.
2. Use the area to find the total cost of cultivation based on the given rate.