Find the area of R if region R is bound by |x| + |y| = 6. Please explain what you did and if you can show me on the cartesian plane so that I have a visual representation. Thanks!

Question

anonymous · Answer

Ther region R is the union of 4 equal right triangles having their right angle at the origin and their other vertices on the axis 6 units away from the origin.
Area = 4 ( 6)(6)/2=72

anonymous · Answer

Thank you, but how do you get that as a graph? Because when I plug in values for x and get y, y for x as well, I only get 1 intersection for some reason.

anonymous · Answer

You have to study the situation in each quadrant:
for example in the first quadrant
$$
x\ge 0\
y\ge  0\
|x|+|y| = x +y = 6
$$
In the second quadrant

$$
x\le 0\
y\ge  0\
|x|+|y| =- x +y = 6
$$
Examine the remaining 2 quadrants and you conclude.

anonymous · Answer

Thank you !