A farmer's land is in the shape of a trapezium which has its parallel sides measuring 2.56 yards and 3.44 yeards and the distance between the parallel sides in 1.44 yards. The cost of ploughing the land is Rs. 1800 per square yard. What amount will (in Rs.) have to be spent in order to plough the entire land ?

Options

A. 3672
B. 6732
C. 7776
D. 8214

Answer

To solve the problem step by step, we will calculate the area of the trapezium and then determine the cost of ploughing the land.

### Step 1: Identify the dimensions of the trapezium
The lengths of the parallel sides are:
- Side 1 (a) = 2.56 yards
- Side 2 (b) = 3.44 yards
The distance between the parallel sides (height, h) = 1.44 yards.

### Step 2: Calculate the area of the trapezium
The formula for the area (A) of a trapezium is given by:
\[ A = \frac{(a + b) \times h}{2} \]
Substituting the values:
\[ A = \frac{(2.56 + 3.44) \times 1.44}{2} \]

### Step 3: Calculate the sum of the parallel sides
First, calculate \(2.56 + 3.44\):
\[ 2.56 + 3.44 = 6.00 \]

### Step 4: Substitute the sum into the area formula
Now substitute this sum back into the area formula:
\[ A = \frac{6.00 \times 1.44}{2} \]

### Step 5: Calculate the area
Now compute \(6.00 \times 1.44\):
\[ 6.00 \times 1.44 = 8.64 \]
Now divide by 2:
\[ A = \frac{8.64}{2} = 4.32 \text{ square yards} \]

### Step 6: Calculate the cost of ploughing
The cost of ploughing per square yard is Rs. 1800. Therefore, the total cost (C) is:
\[ C = A \times \text{cost per square yard} = 4.32 \times 1800 \]

### Step 7: Compute the total cost
Now calculate \(4.32 \times 1800\):
\[ 4.32 \times 1800 = 7776 \text{ Rs.} \]

### Final Answer
The amount that will have to be spent in order to plough the entire land is Rs. 7776.

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