A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the thired side at right angles. The length of the fourth side is 100 m. If it costs Rs. 5 to plough 1 `m^(2)` of the field, find the total cost of ploughing the field.

Explanation

To solve the problem step by step, we need to find the area of the trapezium-shaped field and then calculate the total cost of ploughing it.

### Step 1: Identify the dimensions of the trapezium
The trapezium has:
- Two parallel sides: \( a = 90 \, m \) and \( b = 30 \, m \)
- The height \( h \) can be determined since the trapezium meets the third side at right angles.

### Step 2: Determine the height of the trapezium
Since the sides meet at right angles, we can visualize the trapezium as a rectangle with a triangle on one side. The length of the fourth side is given as \( 100 \, m \).

We can break down the trapezium:
- The longer parallel side is \( 90 \, m \).
- The shorter parallel side is \( 30 \, m \).
- The difference in length between the two parallel sides is \( 90 - 30 = 60 \, m \).

Since the trapezium meets the third side at right angles, we can conclude that the height \( h \) of the trapezium is equal to the length of the fourth side, which is \( 100 \, m \).

### Step 3: Calculate the area of the trapezium
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
Substituting the values:
\[ A = \frac{1}{2} \times (90 + 30) \times 100 \]
\[ A = \frac{1}{2} \times 120 \times 100 \]
\[ A = 60 \times 100 = 6000 \, m^2 \]

### Step 4: Calculate the total cost of ploughing the field
The cost to plough \( 1 \, m^2 \) of the field is \( Rs. 5 \). Therefore, the total cost \( C \) can be calculated as:
\[ C = \text{Area} \times \text{Cost per } m^2 \]
\[ C = 6000 \times 5 \]
\[ C = 30000 \, Rs. \]

### Final Answer
The total cost of ploughing the field is **Rs. 30,000**.

---