Question

Find the area enclosed by the equation |x| + |y| = 4.

• A. 4 squnits
• B. 8 squnits
• C. 16 squnits
• D. 32 squnits

Answer 1

The correct option is D 32 squnits

Given equation, we can write like:

If x $<$ 0 and y $>$ 0, - x + y = 4

If y $<$ 0 and x$>$ 0, x - y = 4

If x $<$ 0 and y $<$ 0, - x - y = 4

If x $>$ 0 and y $>$ 0, x + y = 4

From the above four equations, we can draw below graph.

Above graph is combination of 4 triangle. Area of one triangle = $\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 4\times 4=8$

There are four similar triangle, Area = 8 $\times$ 4 = 32.