Difference between revisions of "2023 AMC 10B Problems/Problem 13"
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| + | ==Problem 13== | ||
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| + | What is the area of the region in the coordinate plane defined by | ||
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| + | <math>| | x | - 1 | + | | y | - 1 | \le 1</math>? | ||
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== Solution == | == Solution == | ||
First consider, <math>|x-1|+|y-1| <= 1.</math> | First consider, <math>|x-1|+|y-1| <= 1.</math> | ||
Revision as of 17:13, 15 November 2023
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 
.
