A farmer's land is in the shape of a trapezium which as 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 need to find the area of the trapezium and then calculate the cost of ploughing based on the area.

### Step 1: Identify the dimensions of the trapezium
The trapezium has:
- Length of the first parallel side (a) = 2.56 yards
- Length of the second parallel side (b) = 3.44 yards
- 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: Simplify the expression
First, calculate the sum of the parallel sides:
\[ 2.56 + 3.44 = 6.00 \]
Now substitute this back into the area formula:
\[ A = \frac{6.00 \times 1.44}{2} \]

### Step 4: Calculate the area
Now calculate:
\[ A = \frac{8.64}{2} = 4.32 \text{ square yards} \]

### Step 5: Calculate the cost of ploughing
The cost of ploughing per square yard is Rs. 1800. Therefore, the total cost (C) is given by:
\[ C = A \times \text{cost per square yard} \]
Substituting the values:
\[ C = 4.32 \times 1800 \]

### Step 6: Perform the multiplication
Now calculate the total cost:
\[ C = 7776 \text{ Rs.} \]

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

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