Parts of three-dimensional figures (Review)

Learning Objectives Identify and count the faces, edges, and vertices of common polyhedra. Differentiate between the altitude (height) and the slant height of a pyramid or cone. Classify three-dimensional figures as polyhedra or non-polyhedra, and name them based on their properties. Define and locate the base(s), lateral faces, and lateral edges of prisms and pyramids. Identify the radius, diameter, and height of cylinders and cones. Apply Euler's formula to verify the relationship between faces, vertices, and edges of a convex polyhedron. Ever wonder how architects design skyscrapers or how video game designers create realistic 3D worlds? 🏙️ It all starts with understanding the basic building blocks of the shapes you see every day! This tutorial will review the funda...

TermDefinitionExample PolyhedronA solid in three dimensions with flat polygonal faces, straight edges, and sharp corners or vertices. It has no curved surfaces.A cube is a polyhedron. A cylinder is not. FaceA flat, polygonal surface of a polyhedron.A rectangular prism has 6 rectangular faces. EdgeA line segment where two faces of a polyhedron meet.A cube has 12 edges of equal length. Vertex (plural: Vertices)A point where three or more edges meet; a corner.A pyramid has a vertex at its apex where all the triangular faces meet. Altitude (Height, h)The perpendicular distance from the base of a figure to its highest point or opposite base.The altitude of a right cylinder is the length of the segment connecting the centers of its two circular bases. Slant Height (l)The distance from the apex...

Euler's Formula for Polyhedra V - E + F = 2 For any convex polyhedron, the number of Vertices (V) minus the number of Edges (E) plus the number of Faces (F) always equals 2. Use this to verify the parts of a polyhedron or to find a missing count if two of the three are known. Pythagorean Theorem for Slant Height h^2 + r^2 = l^2 In a right cone, the altitude (h), radius (r), and slant height (l) form a right triangle with the slant height as the hypotenuse. This formula is used to find a missing dimension when the other two are known. A similar principle applies to right pyramids using the apothem of the base instead of the radius.