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/-
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