SOLUTION: What is the area defined by the following graphs: |x|+|y| is greater than or equal to 2 and |x|+|y| is less than or equal to 5

Algebra ->  Coordinate-system -> SOLUTION: What is the area defined by the following graphs: |x|+|y| is greater than or equal to 2 and |x|+|y| is less than or equal to 5      Log On


   

Question 55186: What is the area defined by the following graphs:
|x|+|y| is greater than or equal to 2 and |x|+|y| is less than or equal to 5
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area defined by the following graphs:
|x|+|y| is greater than or equal to 2
CASE 1 ..X AND Y POSITIVE..WE GET...X+Y>=2
CASE 2...X + VE Y - VE.....WE GET ..X-Y>=2
CASE 3...X -VE..Y -VE......WE GET ..-X-Y>=2
CASE 4...X - VE..Y..+ VE...WE GET ...-X+Y>=2
and |x|+|y| is less than or equal to 5
SAME WAY WE GET HERE X+Y<=5......X-Y<=5......-X-Y<=5.......-X+Y<=5
GRAPH LOOKS LIKE THIS


it is the area of square with side of 5sqrt(2) - area os square with side of 2sqrt(2) = 5*sqrt(2)*5*sqrt(2)-2*sqrt(2)*2*sqrt(2) =50-8=42