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Answer :

32 sq. units Solution :

We have `3 le |x|+|y| le 5`. <br> `|x|+|y| le 5` means that points lie inside the square endpoints of whose diagonal are `(+-5,0) " and " (0,+-5).` <br> `|x|+|y| ge 3` means that points lie outside the square endpoints of whose diagonal are `(+-3,0) " and " (0,+-3).` <br> So, common region is as shown in the figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CG_C02_E04_007_S01.png" width="80%"> <br> `"Area of region" =4((1)/(2) xx 5 xx 5-(1)/(2) xx 3 xx 3) = 32 "sq.units"`