# A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1m² of the field, find the total cost of ploughing the field.

**Solution:**

Given, the field is in the shape of a trapezium

The parallel sides are 90 m and 30 m

The parallel sides meet the third side at right angles

The length of the fourth side is 100 m

We have to find the cost of ploughing the entire field at the rate of Rs. 4/m²

Consider a trapezium ABCD

Draw CE perpendicular to AB

DC = AE = 30 m

EB = AB - AE

EB = 90 - 30

EB = 60 m

Consider right angled triangle BEC,

By using Pythagorean theorem,

BC² = BE² + EC²

(100)² = (60)² + EC²

EC² = 10000 - 3600

EC² = 6400

Taking square root,

EC = 80 m

Area of trapezium = 1/2 × sum of parallel sides × distance between parallel sides

Area of trapezium ABCD = 1/2 × (AB + CD) × EC

= 1/2 × (90 + 30) × 80

= 1/2 × 120 × 80

= 60 × 80

= 4800 m²

Cost of ploughing 1 m² of field = Rs. 4

Cost of ploughing 4800 m² of field = 4800 × 4

= Rs. 19200

Therefore, the cost of ploughing the field is Rs. 19200/-

**✦ Try This: **A field is in the shape of a trapezium having parallel sides 100 m and 40 m. These sides meet the third side at right angles. The length of the fourth side is 120 m. If it costs Rs 5 to plough 1m² of the field, find the total cost of ploughing the field.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.4 Problem 5**

## A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1m² of the field, find the total cost of ploughing the field.

**Summary:**

A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1m² of the field, the total cost of ploughing the field is Rs. 19200/-

**☛ Related Questions:**

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