The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]
- 3 Square units
- 2 Square units
- 5 Square units
- 4 Square units
The Correct Option is A
Approach Solution - 1
The graph of \(|x|-y≤1,y≥0\) and \(y≤1\) is as follows:
To find the area of quadrilateral ABCD, we subtract the areas of triangles EAD and BFC from the area of rectangle EFCD:
Area of ABCD = Area of EFCD − Area of △EAD − Area of △BFC
Using the formula:
\( \text{Area of ABCD} = EF \times FC - \frac{1}{2} \times EA \times ED - \frac{1}{2} \times BF \times FC \)
Substituting the values:
\( = 4 \times 1 - \frac{1}{2} \times 1 \times 1 - \frac{1}{2} \times 1 \times 1 \)
\( = 4 - 0.5 - 0.5 = 3 \) square units
Final Answer: \( \boxed{3} \) square units
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 option is (A) : 3 Square units.
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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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