Final answer:
The Geometric period in Ancient Greece is responsible for triangle-shaped design.
Step-by-step explanation:
The culture responsible for triangle-shaped design is the Geometric period in Ancient Greece, which lasted from approximately 900 BCE to 700 BCE. This period witnessed the emergence of a new culture on the Greek mainland, characterized by the proliferation of geometric designs and rendering of figures in art.
The Geometric period saw the use of triangles in various forms, such as in the shapes and patterns of pottery and the representation of human figures.