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

Answer: (C)

8

Answer 2

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 $= \frac{1}{2}(4)(4)=8$