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Find the area of the region formed by th...

Find the area of the region formed by the points satisfying
`|x| + |y| + |x+y| le 2.`

Text Solution

Verified by Experts

The correct Answer is:
16
`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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