Lesson 3 — Polygons and Polyhedra: Pyramid Architecture
Big idea: A polygon is a flat closed figure made of straight sides. A polyhedron is a 3D solid whose faces are polygons.
Words to know
| Word | Meaning |
|---|---|
| Polygon | A figure bounded by line segments that lies in a plane. |
| Polyhedron | A figure bounded by polygons that exists in space. |
| Triangle | 3-sided polygon. |
| Quadrilateral | 4-sided polygon. |
| Pentagon | 5-sided polygon. |
| Hexagon | 6-sided polygon. |
| Octagon | 8-sided polygon. |
| Perimeter | The sum of the lengths of the sides of a polygon. |
| Area | The number of unit squares that cover a surface. |
| Rectangle | A quadrilateral with four right angles. |
| Square | A rectangle with all four sides equal. |
Concepts to know
- A line segment is one-dimensional.
- A polygon is two-dimensional and lies in a plane.
- A polyhedron is three-dimensional.
- A polygon’s perimeter is a distance; its area is a surface.
- A square is a special rectangle, so every square is a rectangle.
- A polyhedron has faces (polygons), edges (where faces meet), and vertices (corners).
- A square pyramid has 5 faces, 8 edges, and 5 vertices.
Formulas
| Shape | Formula |
|---|---|
| Any polygon | P = sum of all side lengths |
| Rectangle | A = lw |
| Square | A = s² |
| Square | P = 4s |
Homework helper
| If the homework asks… | Do this… |
|---|---|
| Name a polygon | Count the sides: 3 triangle, 4 quadrilateral, 5 pentagon, 6 hexagon, 8 octagon. |
| Find perimeter | Add every side length. |
| Find area of a rectangle | Multiply length by width. |
| Find area of a square | Square one side. |
| Find a missing side from area | Use the inverse operation; for a square, take the square root. |
| Count faces, edges, vertices | Count carefully; do not forget the base. |
| Work with a scale model | Set up a proportion between model and real lengths. |
Worked example
The Great Pyramid’s square base has sides of 756 feet.
Perimeter = 4 × 756 = 3,024 feet
Area = 756 × 756 = 571,536 square feetA square pyramid has 5 faces (1 square base + 4 triangles), 8 edges, and 5 vertices.
Watch out
- Perimeter and area have different units: feet vs. square feet.
- Do not call every rectangle a square; only squares have four equal sides.
- The base of a pyramid is a face, so count it.
- Area is not the same as perimeter, even if the numbers look similar.