GATE CS 2021 Set 1 Q2 — General Aptitude

By definition, a polygon is convex if the line segment connecting any two points inside the polygon lies entirely inside or on the boundary of the polygon. Conversely, a polygon is non-convex (concave) if we can find at least one pair of points $P$ and $Q$ inside the polygon such that the line segment $PQ$ passes outside the polygon.

• Option A: This shape contains one or more reflex angles (interior angles greater than $180^\circ$). If we choose two points $P$ and $Q$ near the inward-pointing corners, the line segment $PQ$ connecting them goes outside the boundary of the shape. Therefore, it is NOT a convex polygon.
• Options B, C, and D: These are all convex polygons because all their interior angles are less than $180^\circ$. Any line segment drawn between any two points inside these shapes will lie entirely within the shape.

Thus, the polygon in Option A is not convex.