Classification of Prisms and Pyramids
Prisms and pyramids are 3D shapes defined by their base. A rectangular prism has a rectangular base (and 6 rectangular faces total). A triangular prism has a triangular base. A pyramid has any polygon as a base, with triangular faces meeting at an apex. The key classification is base shape: the base names the prism or pyramid. Quadrilateral classification deepens the understanding of polygon attributes: a square is a special rectangle which is a special parallelogram which is a special quadrilateral.
Prisms: defined by their base
A prism has two congruent, parallel bases connected by rectangular faces. The base shape names the prism: rectangular prism (box shape), triangular prism (Toblerone shape), hexagonal prism (honeycomb cell). Key property: any cross-section parallel to the base has the same shape and size as the base. This is why volume = base area x height works for all prisms.
Quadrilateral hierarchy
All quadrilaterals are four-sided polygons. Parallelograms have two pairs of parallel sides: includes rectangles, rhombuses, and squares. Rectangles have four right angles: includes squares. Rhombuses have four equal sides: includes squares. A square is both a rectangle and a rhombus. A trapezoid has exactly one pair of parallel sides: it is a quadrilateral but not a parallelogram.
Prisms in the environment
Rectangular prisms: buildings, books, cereal boxes. Triangular prisms: Toblerone chocolate, tent shapes, Pythagorean theorem wedges. Hexagonal prisms: honeycomb cells (strongest shape for a given amount of material). Pyramids: Egyptian pyramids (square base), Mayan temples (stepped square base), First Nations ceremonial structures. Identifying 3D shapes in the environment connects geometry to design thinking.