Ployhedrons
Polyhedrons: solid with flat faces, "poly" meaning many "hedron" face.
Platonic solids: a 3D shape that has each face the same regular polygon and the same number of polygons meet at each vertex.
Five different platonic solids:
Tetrahedron:
- 3 triangles meet at each vertex
- 4 faces
- 4 vertices
- 6 edges
Cube:
- 3 squares meet at each vertex
- 6 faces
- 8 vertices
- 12 edges
Octahedron:
- 4 triangles meet at each vertex
- 8 faces
- 6 vertices
- 12 edges
Dodecahedron:
- 3 pentagons meet at each vertex
- 12 faces
- 20 vertices
- 30 edges
Icosahedron:
- 5 triangles meet at each vertex
- 20 faces
- 12 vertices
- 30 edges
Three-dimensional solids
- Surface area of a cube: Surface Area = 6 × (Edge Length)2
- Surface area of a tetrahedron: √3 × (Edge Length)2
- Surface area of a octahedron: Surface Area = 2 × √3 × (Edge Length)2
- Surface area of a dodecahedron: Surface Area = 3×√(25+10×√5) × (Edge Length)2
- Surface area of a Icosahedron: Surface Area = 5×√3 × (Edge Length)2
Lateral Area
The lateral area is the surface area of a 3D figure
Lateral area of a right prism: perimeter*height
Lateral area of a right prism: perimeter*height
Lateral area of a right cylinder: Circumference*height
Lateral area of a regular pyramid: 1/2 perimeter*slant height
Lateral area of right circular cone: 1/2 perimeter*slant height
Surface area
Surface area of a regular pyramid: Base area + 1/2*perimeter*slant height
Surface area of a right circular cone: 4pr2
Surface area of a right circular cone: 4pr2
Volume
Volume of right prism and a right cylinder: base area*height
Volume of pyramid and circular cone: 1/3*base area*height
Congruent solids
Properties:
All angles are congruent, corresponding edges are congruent, all faces and volumes are congruent.
All angles are congruent, corresponding edges are congruent, all faces and volumes are congruent.
Similar solids
Similar solids have the same shape but not always the same size
