2023 AMC 10B Problems/Problem 13
Problem 13
What is the area of the region in the coordinate plane defined by
?
Solution
First consider,
We can see that it's a square with radius 1 (diagonal 2). The area of the square is
Next, we add one more absolute value and get This will double the square reflecting over x-axis.
So now we got 2 squares.
Finally, we add one more absolute value and get This will double the squares reflecting over y-axis.
In the end, we got 4 squares. The total area is
~Minor formatting change: e_is_2.71828