Pyramid practice problems - page 9 of 13

A pyramid is a three-dimensional geometric shape with a polygonal base and triangular faces that meet at a common point called the apex (or vertex). The base can be any polygon (e.g., triangle, square, pentagon), and the shape of the pyramid is often named after its base. For example:
- A triangular pyramid has a triangular base.
- A square pyramid has a square base.
- A pentagonal pyramid has a pentagonal base.

Key Features of a Pyramid:

1. Base: The polygonal face at the bottom.
2. Faces: The triangular sides connecting the base to the apex.
3. Apex: The topmost point where all the triangular faces meet.
4. Edges: The lines where two faces meet.
5. Height (h): The perpendicular distance from the base to the apex.

Formulas for a Pyramid:

1. Volume (V):

V = 1/3 × Base Area × Height

The volume is one-third of the product of the base area and the height.

2. Surface Area (SA):
Lateral Surface Area (LSA): The sum of the areas of the triangular faces.
Total Surface Area (TSA): The sum of the lateral surface area and the base area.