1. The problem asks which shapes can be set up in a cookie shaper machine and what these shapes have in common. 2. Convex polygons like the pentagon, hexagon, and octagon can be set up in the cookie shaper machine because all their interior angles are less than 180 degrees, making them simple and stable shapes. 3. Concave polygons such as the crescent moon, cross, star, lightning bolt, and heart shapes have at least one interior angle greater than 180 degrees, which makes them complex and difficult to shape consistently. 4. Convex polygons have the property that a line segment between any two points in the polygon lies entirely inside it. This is important for cookie shaping machines to cut cleanly. 5. Among the convex polygons, the regular pentagon, hexagon, and octagon can have equal side lengths and equal interior angles. For example, a regular hexagon has all sides and angles equal. 6. The concave shapes look more complicated because they have indentations or inward curves, making their geometry more complex and harder to produce uniformly. 7. Producing different shapes of cookies impacts consumers by offering variety and aesthetic appeal, but complex shapes may increase production cost and breakage. Final answer: - Shapes suitable for cookie shaper machine: pentagon, hexagon, octagon (convex polygons). - Common property: all interior angles less than 180 degrees, no indentations. - Shapes with equal side lengths and angles: regular pentagon, regular hexagon, regular octagon. - More complicated shapes: concave polygons like star, crescent moon, cross, lightning bolt, heart. - Impact: variety and appeal vs. production complexity and cost.