Questions: Concave or convex Regular OR Irregular

Solution Steps

To determine if a polygon is concave or convex, we need to check the internal angles. A polygon is convex if all its internal angles are less than 180 degrees. For regular or irregular classification, a polygon is regular if all its sides and angles are equal.

To determine if the polygon defined by the vertices \((0, 0)\), \((2, 0)\), \((2, 2)\), and \((0, 2)\) is convex, we check the internal angles. Since all internal angles are less than \(180^\circ\), we conclude that the polygon is convex.

Next, we check if the polygon is regular. A polygon is regular if all its sides are equal in length. The lengths of the sides are calculated as follows:

• Length between \((0, 0)\) and \((2, 0)\): \(2 - 0 = 2\)
• Length between \((2, 0)\) and \((2, 2)\): \(2 - 0 = 2\)
• Length between \((2, 2)\) and \((0, 2)\): \(2 - 0 = 2\)
• Length between \((0, 2)\) and \((0, 0)\): \(2 - 0 = 2\)

Since all sides are equal to \(2\), the polygon is regular.

Final Answer