Question:
The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is
The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is
Updated On: Apr 29, 2024
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Approach Solution - 1
The graph of \(|x|-y≤1,y≥0\) and \(y≤1\) is as follows:
Area of ABCD = Area of EFCD - Area of EAD - Area of BFC
= \(EF×FC-\frac{1}{2}×EA×ED-\frac{1}{2}×BF×FC\)
= \(4×1-\frac{1}{2}×1×1-\frac{1}{2}×1×1\)
= \(4-1 = 3\) Square units
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Approach Solution -2
Area of the region contained by the lines | x | -y ≤ 1, y ≥ 0 and y ≤ 1 is the two triangle and the one rectangle in white region.
So, we have calculate these area to get the total area.
Total Area = Area of rectangle + 2 × Area of triangle
= \(2+(\frac{1}{2}\times2\times1)=3\)
Therefore, the correct answer is 3.
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