Lesson 5: Surface Area

Property

Every polyhedron is constructed from three basic parts:

• Faces: The flat polygonal surfaces of the solid.
• Edges: The straight line segments formed where two faces intersect.
• Vertices: The corner points where three or more edges meet.

Examples

• A cube has 6 faces (squares), 12 edges, and 8 vertices.
• A triangular prism has 5 faces total (2 triangular bases + 3 rectangular sides), 9 edges, and 6 vertices.
• A triangular pyramid has 4 faces (all triangles), 6 edges, and 4 vertices.

Explanation

To break down any 3D shape, just count its parts! Faces are the flat sides you can touch, edges are the straight lines you can trace with your finger, and vertices are the pointy corners. Counting these components is the first step to classifying any 3D figure.

Property

Polyhedra are split into two main families based on how they are built:

• Prism: A 3D figure with 2 parallel, congruent polygons as bases. The lateral faces connecting the bases are flat rectangles or parallelograms.
• Pyramid: A 3D figure with exactly 1 polygon base. All other flat faces are triangles that connect to a single point at the top called the apex.

Examples

• A rectangular prism (like a shoebox) has 2 rectangular bases and 4 rectangular lateral faces.
• A triangular prism, like a tent, has 2 triangular faces as bases and 3 rectangular faces as sides.
• A square pyramid has one square base and four triangular faces that meet at the top apex.

Explanation

Prisms are like shapes that have been 'stretched' straight up; whatever shape is on the bottom floor matches the top ceiling exactly. Pyramids only have a bottom floor, and their walls lean inward to meet at a single sharp point at the very top.