Question

What is the area enclosed? Please explain how. Thanks in advance

Answer 1

So your function yields the following graph:

graph{|x-1|+|y-1|=1 [-1.62, 3.668, -0.36, 2.284]}

As we can see, this creates a small square. However, the side lengths are not just 1. The first thing we need to do is find the sides. We can do this with triangles.

By connecting the points at (0,0), (1,0), and (0,1), we have a triangle with two legs of one unit. We can now use Pythagorean Theorem to get the length of the hypotenuse, which is the side length of our square:

`a^2+b^2=c^2`

`sqrt(a^2+b^2)=c`

`sqrt(1^2+1^2)=c`

`c=sqrt(2)`

Therefore, we know the side lengths of the square are all `sqrt(2)` units. So now we want the area. Since we know this is a square, all sides are equal, so we just need to multiply one of the legs by itself (If you want a proof that this is a square, you can find one of the lengths of the adjacent squares and making sure it's also `sqrt(2)` units long).

`A=s^2`

`A=sqrt(2)^2`

The square root and the square cancel out.

`A=2`

`therefore` The area of the enclosed square is 2 `"units"^2`.