Question

13.Area enclosed between the lines x+2y-4 =0 and x+2y-2 =0 and the coordinate axes is​

Answer 1

Given :  the lines x+2y-4 =0 and x+2y-2 =0  

To Find : Area enclosed between the lines x+2y-4 =0 and x+2y-2 =0 and the coordinate axes

Solution:

x+2y-4 =0  and  x+2y-2 =0   are parallel lines

x+2y-4 =0  

intersection with  x & y axis

(0 , 2)  and ( 4 , 0)

x+2y-2 =0

intersection with  x & y axis

(0 , 1)  and ( 2 , 0)

Area between  lines x+2y-4 =0 and x+2y-2 =0 and the coordinate axes is​

= Area of Triangle by  (0 , 0) , ( 4 , 0) , ( 0 , 2)  - Area of Triangle by  (0 , 0) , ( 2 , 0) , ( 0 , 1)

Area of Triangle by  (0 , 0) , ( 4 , 0) , ( 0 , 2)  = (1/2) (4 * 2)  = 4

Area of Triangle by  (0 , 0) , ( 2 , 0) , ( 0 , 1)  = (1/2) (2 * 1)  =  1

Area between  lines x+2y-4 =0 and x+2y-2 =0 and the coordinate axes is​

= 4 - 1

= 3 Sq units

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