Question

The area of the closed region bounded by the equation \(| x | + | y | = 2\) in the two-dimensional plane is

• A. \( 4\pi\)
• B. 4
• C. 8
• D. \( 2\pi\)

Answer 1

The Correct Option is C

The area enclosed by the equation \(∣ax∣+∣by∣=c\) in the two-dimensional plane is \(±\frac{c}{|a|}\) and y- intercepts of \(±\frac{c}{|b|}\)
In general, it forms a rhombus. However, in the given scenario, we have a square with diagonals each measuring 4 units.

Area \(= \frac{1}{2}(4)(4)=8\)