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Find the area of the region in which poi...

Find the area of the region in which points satisfy
`3 le |x| + |y| le 5.`

Text Solution

Verified by Experts

The correct Answer is:
32 sq. units
We have `3 le |x|+|y| le 5`.
`|x|+|y| le 5` means that points lie inside the square endpoints of whose diagonal are `(+-5,0) " and " (0,+-5).`
`|x|+|y| ge 3` means that points lie outside the square endpoints of whose diagonal are `(+-3,0) " and " (0,+-3).`
So, common region is as shown in the figure.

`"Area of region" =4((1)/(2) xx 5 xx 5-(1)/(2) xx 3 xx 3) = 32 "sq.units"`
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