Absolute value problem 2 by Dhaval Furia

Geometry Level pending

Let $S$ be the set of all points $(x, y)$ in the $xy$ -plane such that $| x | + | y | ≤ 2$ and $| x | ≥ 1$ . Find the area of the region represented by $S$ .

The answer is 2.

2 solutions

Chew-Seong Cheong
Jun 13, 2020

$|x|+|y| \le 2$ is the region within a square with side length $\sqrt 2$ and diagonals parallel to the axes (blue square). The condition $|x| \ge 1$ limits the region to the two corners $x \le -1 \cup x \ge 1$ , so the area is that of two halves of a square of side length $\sqrt 2$ or $(\sqrt 2)^2 = \boxed 2$ .

@Dhaval Furia(https://brilliant.org/profile/dhaval-s13ger/), try not to end all problems with a red underscore line. It is more professional to use a proper English like most other problems if not all in Brilliant. You may find it interesting that the line appears red but red in LaTex means error. I am a moderator and I have been changing all your problems. Continue to enjoy Brilliant.

Chew-Seong Cheong - 12 months ago

A Former Brilliant Member
Jun 12, 2020

The given region is a pair of triangles with sides of length $2,\sqrt 2, \sqrt 2$ each. The area required is $2\times \dfrac {1}{2}\times 2\times 1=\boxed 2$ square units.

Absolute value problem 2 by Dhaval Furia

The answer is 2.

2 solutions

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