### Home > INT3 > Chapter 3 > Lesson 3.2.3 > Problem3-102

3-102.

Make a complete graph of the system of inequalities below.

$\left. \begin{array} { l } { y \geq | x | - 3 } \\ { y \leq - | x | + 5 } \end{array} \right.$

1. What polygon is formed?

The polygon looks like it has perpendicular sides. What are the slopes of the sides?
Does this tell you they are perpendicular?

2. What are its vertices?

Look at the graph to find the vertices.

3. What is the area of the enclosed polygon?

Each side of the polygon is the hypotenuse of a right triangle with side lengths of $4$.

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Int3 3-102 HW eTool