Count vertices, edges, and faces

Key Notes:

Basic Shapes and Their Parts:

• Solid Shapes (3D): These shapes take up space and have three dimensions (length, width, height). We can count their vertices, edges, and faces.
• Vertex (Vertices):
  • A corner where two or more lines (edges) meet.
  • Think of it as the “pointy” part of a shape.
  • Example: The corner of a box.
• Edge:
  • A line segment where two faces of a solid shape meet.
  • Think of it as the “side” or “line” of a shape.
  • Example: The line where two sides of a box connect.
• Face:
  • A flat surface of a solid shape.
  • Think of it as the “flat part” you can touch.
  • Example: One side of a box.

II. Common Solid Shapes :

• Cube:
  • Looks like a box where all sides are squares.
  • Vertices: Count all the corners (8).
  • Edges: Count all the lines where the sides meet (12).
  • Faces: Count all the square sides (6).
• Cuboid (Rectangular Prism):
  • Looks like a box (can be long or short). All faces are rectangles.
  • Vertices: Count all the corners (8).
  • Edges: Count all the lines where the sides meet (12).
  • Faces: Count all the rectangular sides (6).
• Sphere:
  • Looks like a ball.
  • Vertices: 0 (no corners).
  • Edges: 0 (no straight lines).
  • Faces: 1 curved surface.
• Cylinder:
  • Looks like a can or a tube. It has two flat circular ends and one curved surface.
  • Vertices: 0 (no pointy corners).
  • Edges: 2 circular edges where the flat ends meet the curved surface.
  • Faces: 3 (2 flat circles, 1 curved surface).
• Cone:
  • Looks like an ice cream cone or a party hat. It has one flat circular base and one curved surface that comes to a point.
  • Vertices: 1 (the pointy top).
  • Edges: 1 circular edge where the base meets the curved surface.
  • Faces: 2 (1 flat circle, 1 curved surface).

III. How to Count:

• Vertices: Carefully point to each corner as you count.
• Edges: Carefully trace along each line where two faces meet as you count. It can be helpful to mark each edge as you count it to avoid double-counting.
• Faces: Carefully count each flat surface. For curved surfaces (like on a sphere, cylinder, or cone), identify them as one continuous face.

Learn with an example

let’s practice! 🖊️