Which architectural style is characterized by its simplistic design and use of local materials?

The correct answer is Vernacular architecture. This style is distinguished by its emphasis on practicality and the use of locally available materials, which often leads to designs that are deeply reflective of the cultural and environmental context in which they were built. Vernacular architecture does not adhere to formal styles; instead, it is shaped by the needs, beliefs, and traditions of the local population.

Craftsman, while also focused on craftsmanship and the use of local materials, features more intricate designs and details such as exposed beams and built-in furniture, setting it apart from the more straightforward aesthetics of vernacular buildings. Colonial Revival architecture seeks to emulate earlier American building styles, often resulting in more ornamental and formal characteristics, which distracts from the simplicity found in vernacular buildings. Federal architecture, associated with the period following the American Revolution, often showcases classical elements and symmetry, diverging from the pragmatic and simplistic nature typical of vernacular design. Hence, the characteristics of simplistic design and local material use are best exemplified by vernacular architecture.