1. Pyramid
• Given a polygonal region R in a plane E and a point V
not in E, the pyramid with base R and vertex V is the
union of all line segments such that N is a point of R.
• Most of the pyramids that are studied in high school
are regular pyramids. These pyramids have the
following characteristics:
• 1) The base is a regular polygon.
• 2) All lateral edges are congruent.
• 3) All lateral faces are congruent isosceles triangles.
• 4) The altitude meets the base at its center.
• The altitude of a lateral face of a regular pyramid is the
slant height. In a non-regular pyramid, slant height is
not defined.
2. Lateral Surface Area
• The lateral surface area of a regular
pyramid is the sum of the areas of its lateral faces.
The general formula for the lateral
surface area of a regular pyramid is
where p represents the perimeter of the base
and l the slant height.
3. Right vs Oblique Pyramid
• This tells you where the top (apex) of the pyramid is. If the
apex is directly above the center of the base, then it is a Right
Pyramid, otherwise it is an Oblique Pyramid.
Right pyramid Oblique Pyramid
4. Regular vs Irregular Pyramid
This tells us about the shape of the base. If the base is a regular
polygon, then it is a Regular Pyramid, otherwise it is an
Irregular Pyramid.
Base is Regular Base Is Irregular
5. Part Of Pyramid
Triangular Pyramid
Characteristic: a. It has 4 Faces
b.The 3 Side Faces are Triangles
c.The Base is also a Triangle
d. It has 4 Vertices (corner points) It
has 6 Edges.
Volume = 1/3 × [Base Area] × Height .
Surface Area (when all side faces are the same):
= [Base Area] + 1/2 × Perimeter × [Side Length]
6. Square Pyramid
• Characteristic : a. It has 5 Faces
b. the 4 Side Faces are Triangles
c. the Base is a Square
d. It has 5 Vertices (corner points)
e. It has 8 Edges
• Surface Area = [Base Area] +1/2 × Perimeter ×
[Slant Length]
• Volume = 1/3 × [Base Area] × Height
7. Pentagonal Pyramid
• Characteristic: a. It has 6 Faces
b. The 5 Side Faces are Triangles
c. The Base is a Pentagon
d. It has 6 Vertices (corner
points)
e. It has 10 Edges
• Volume = 1/3 × [Base Area] × Height
• Surface Area (when all side faces are the same):
= [Base Area] + 1/2 × Perimeter × [Side Length]
