Question

What is the sum of the number of vertices, edges, and faces of a triangular pyramid?

• A. $14$
• B. $12$
• C. $8$
• D. $15$

Answer 1

The correct option is A $14$

A triangular pyramid has one triangular base and three triangular sides.

Vertices (where two or more lines meet)$:4$
There are three vertices on the base (one at each corner of the square) and a fourth at the top of the pyramid.

Edges (line segment joining two vertices)$:6$
There are three edges on the base (one along each side) and three more along the sides of the triangular faces extending from the corners of the base to the top vertex.

Faces (planar surfaces)$:4$
The base is one face, and there are three triangular faces that form the top of the pyramid.

$\therefore \text{Number of vertices + Number of edges}\text{+ Number of faces}=4+6+4=14$