Question

which is a correct description of the polygon?
it is a concave pentagon because segment ae would extend into the inside of the polygon, and it has five sides.
it is a convex hexagon because it has six sides and none of the sides would extend into the inside of the polygon.
it is a concave hexagon because segment ae would extend into the inside of the polygon, and it has six sides.
it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

Explanation:

• Count the number of sides: The polygon has vertices \(A\), \(B\), \(C\), \(D\), \(E\), so it has \(5\) sides. A polygon with \(5\) sides is a pentagon.
• Determine convex or concave: A concave polygon has at least one interior angle greater than \(180^{\circ}\), which means a line segment (like \(AE\) in this case) can be drawn such that it extends into the interior of the polygon.

Answer:

It is a concave pentagon because segment \(AE\) would extend into the inside of the polygon, and it has five sides.