Question:medium

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]

Updated On: Jan 15, 2026
  • 3 Square units
  • 2 Square units
  • 5 Square units
  • 4 Square units
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The Correct Option is A

Solution and Explanation

The graph representing the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is displayed below:
The graph of (|x|-y<=1,y>=0) and (y<=1)

To determine the area of quadrilateral ABCD, the areas of triangles EAD and BFC are subtracted from the area of rectangle EFCD:

Area of ABCD = Area of EFCD − Area of △EAD − Area of △BFC 

The formula used is:
\( \text{Area of ABCD} = EF \times FC - \frac{1}{2} \times EA \times ED - \frac{1}{2} \times BF \times FC \)

Substituting the given values yields:
\( = 4 \times 1 - \frac{1}{2} \times 1 \times 1 - \frac{1}{2} \times 1 \times 1 \)

\( = 4 - 0.5 - 0.5 = 3 \) square units

Final Answer: \( \boxed{3} \) square units

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