Recognition of Solids
71. The Pyramid's Peak · base, faces, and a common vertex
P is the common vertex of all triangular side faces.
A pyramid is a 3D solid with a polygon base and triangular side faces that all meet at a single point — the apex P. Named by the base: triangular pyramid (tetrahedron), square pyramid, etc.
What this lesson covers
Try to break it
Can you spot the base? It's the quadrilateral ABCD at the bottom. The four triangles PAB, PBC, PCD, and PDA are the side faces. They all share the common vertex P.
How you build it
Construct a pyramid.
- Place point A, the first corner of the base.
- Place point B, the second corner of the base.
- Place point C, the third corner of the base.
- Place point D, the fourth corner of the base.
- Draw the base side from A to B.
- Draw the base side from B to C.
- Draw the base side from C to D.
- Draw the base side from D to A to close the base ABCD.
- Place point P, the apex, above the base.
- Draw the slant edge from P to A.
- Draw the slant edge from P to B.
- Draw the slant edge from P to C.
- Draw the slant edge from P to D to complete the pyramid.
The proof, step by step
Prove that every side face of the pyramid meets at the apex P.
- The base of a pyramid is a plane rectilinear figure.
- All side faces are triangles.
- All side faces meet at a common vertex.
Worked example
A pyramid has a square base and four triangular faces. What is the total number of faces?
A pyramid has 1 base + 4 triangular side faces = 5 faces total.
- 4
- 5 — correct
- 6
- 8