# Surface of Angular Land

ghostfirefox
The area of ​​Angular Land is described by inequalities | x + 5y − 28 | ≤30 and | 3x + 5y −34 | ≤30, where the point with coordinates (x, y) is the point distant x kilometers east of a certain reference point (in the case of x negative, this is a point | x | kilometers west) and y kilometers north (or | y | kilometers south in the case of negative y) from this reference point. The altitude of the point of the Angular Land with coordinates (x, y) expressed in meters above sea level is given by the formula h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |. Calculate the area of ​​Angular Land lying in depression (i.e. below sea level). Enter the integer part of this number.

Homework Helper
Gold Member
Have you graphed what the xy region looks like? Have you had calculus and change of variables in integrals?
Your formula for h doesn't make any sense. Please check that and type it correctly. Also, where did this problem come from?

Homework Helper
Unfortunately there seem to be several "typos" in this. You say you are given that the height above sea level at point (x, y) is given by
h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |.
I will assume that the first "||" is a typo and it should be just "|" but then I have no idea how to interpret "-15|- 3- |x+ 5y- 28|".

Homework Helper
MHB
Unfortunately there seem to be several "typos" in this. You say you are given that the height above sea level at point (x, y) is given by
h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |.
I will assume that the first "||" is a typo and it should be just "|" but then I have no idea how to interpret "-15|- 3- |x+ 5y- 28|".

Looks like it is not a typo.
It is:
$$h = 2 \Big|| x + 5y − 28 | + | 3x + 5y − 34 | −15 \Big| −3− | x + 5y -28 | - | 3x + 5y-34 |$$

Hi ghostfirefox, welcome to MHB!

What are the mathematical tools that you are supposed to use?
Are you for instance familiar with coordinate transformations and the Jacobian to make them work?
Or should we limit ourselves to multiple integrals with variable boundaries?

ghostfirefox
Hi, I don't know how to do this exercise. I have only content from the first post. H is probably
$$h = 2 \Big|| x + 5y − 28 | + | 3x + 5y − 34 | −15 \Big| −3− | x + 5y -28 | - | 3x + 5y-34 |$$

as Klass said