1.

A point P (x,y)moves in in xy plane in such a way that sqrt(2) le |x + y| + |x - y| le 3sqrt(2) . Area of region representing all possible position of point P is equal to:

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Solution :`1LE|(x+y)/(SQRT2)|+|(x-y)/(sqrt2)|LE3`
`1le|X|+|Y|le3""("Rotation through an angle of "(PI)/(4))`
`"Area "=4((1)/(2)xx3xx-(1)/(2)xx1xx1)`
`=4[(9)/(2)-(1)/(2)]`
`=16"(unit)"^(2)`


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