Q29 of 45 Page 1

Using the method of integration, find the area of the region bounded by the following lines:

3x - y - 3 = 0


2x + y - 12 = 0


x - 2y - 1 = 0

The given lines are


⇒ 3x – y -3 = 0


⇒ y = 3x – 3 … (1)


⇒ 2x + y – 12 = 0


⇒ y = 12 - 2x … (2)


⇒ x – 2y – 1 = 0


⇒ y = (x – 1)/ 2 … (3)


For line (1), table:



For line (2), table:



For line (3), table:



Drawing these lines (1), (2) and (3), we get the graph:



These lines intersect at A (3, 6), B (1, 0) and C (5, 2)


∴ Area of ΔABC = area BAL + area LACM – area BCM







= 6 + 8 – 4


= 10 sq. units.


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