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 → B → F → E.
Order is important — face ABEF does not exist here.
Face area = area of one face
Surface area = total area of all faces
To answer questions involving planes, think about using Pythagoras’ Theorem.
\[ AC^2 = AD^2 + DC^2 \]
Shapes made with a uniform cross‑section are called prisms.
Volume of a prism: \[ V = A h \] where \(A\) is the area of the cross‑section.
Made from a square base.
8 vertices, 12 edges, 6 faces.
Area of square: \[ A = l^2 \] Volume of cube: \[ V = l^3 \]
Made from a rectangular base.
8 vertices, 12 edges, 6 faces.
Area of rectangle: \[ A = l b \] Volume of cuboid: \[ V = l b h \]
Made from a triangular base.
6 vertices, 9 edges, 5 faces.
Area of triangle: \[ A = \frac12 b h \] Volume of triangular prism: \[ V = \frac12 b h l \]
Made from a circular base.
0 vertices, 2 edges, 3 faces.
Area of circle: \[ A = \pi r^2 \] Volume of cylinder: \[ V = \pi r^2 h \]
Made from a pentagonal base.
10 vertices, 15 edges, 7 faces.
Made from a hexagonal base.
12 vertices, 18 edges, 8 faces.
Made from an octagonal base.
16 vertices, 24 edges, 10 faces.
© Alexander Forrest