3d shapes

• Terminology

 

Vertices are corners.
Edges are made by joining vertices.
Faces are made by joining edges.

AB means the edge starting at A and finishing at B.

Face ABFE joins A to B to F to E.

Order is important - Face ABEF does not exist here.

 

Face Area  =  Area of the face
Surface Area =    Total area of all the faces 

• Planes

 

To answers questions to do with planes,
think about using Pythagoras’ Theorem.
e.g. (AC)² =(AD)²  +  (DC)²

• Prisms

Shapes made with a uniform cross section are called prisms.
Volume of a prism = Area x Height 
V = Ah

Examples

• Cube

Made from a square base.

                        

     8 vertices, 12 edges, 6 faces
                        

Area  of Square = length x breadth = l²
so Volume of cube  =  Ah = l²x h = l³  units³

 

• Cuboid

Made from a Rectangular base

                    

8 vertices, 12 edges, 6 faces

                      

Area  of rectangle = length x breadth = lb
so Volume  of cuboid =  Ah = lbh units³

 

• Triangular prism

Made from a triangular base

 6 vertices, 9 edges, 5 faces

 

Area  of triangle = ½ x base x perpendicular height =  ½bh
so Volume of triangular prism  =  Ah =½bhl units³
( where l is the length of the prism)

 

• Cylinder

Made from a circular base

0 vertices, 2 edges, 3 faces

       

Area  of circle = π x radius x radius =  π r²
so Volume of cylinder  =  Ah = π r²  units³

 

• Pentagonal Prism

Made from a pentagonal base.

    10 vertices, 15 edges, 7 faces

         

 

• Hexagonal Prism

Made from a hexagonal base.

12 vertices, 18 edges, 8 faces

 

 

• Octagonal Prism

Made from an octagonal base.

    16 vertices, 24 edges, 10 faces