Honors Geometry Section 7.3
Surface Area & Volume of
Pyramids
A pyramid is a 3-dimensional object
consisting of 1 base, which must be a
polygon, and three or more lateral
faces which are triangles.
The lateral faces share a single vertex
called the ______
vertex of the pyramid.
Base edge and lateral edge are defined
in the same way they were for prisms.
vertex
lateral edge
lateral face
base
base edge
As we did with prisms, pyramids
are named by the shape of their
base.
The altitude of a pyramid is the
segment from the vertex
perpendicular to the base.
The height of the pyramid is the
length of the altitude.
The length of an altitude of a
lateral face (i.e. the altitude of a
triangular face) is called the slant
height of the pyramid.
altitude
or
height
Slant
height
A regular pyramid is a pyramid
whose base is a regular polygon
and whose lateral faces are
congruent isosceles triangles.
In a regular pyramid the altitude
intersects the base at its ______
center
and the slant height intersects the
base edge at its ________.
midpoint
You should always assume a
pyramid is a regular pyramid unless
told otherwise.
Volume of a Pyramid = 1/3 x area
of the base x the height of the
pyramid
Example 1: The pyramid of Khufu is a
regular square pyramid with a base edge of
776 feet and a height of 481 feet. What is
the volume of the pyramid?
1
2
V  (776 )(481)
3
V  96,548,885. 3 ft
3
Consider a regular square
pyramid whose slant height
is l and whose base edge is s.
The area of each triangle
½sl
of the net is _______
The lateral area is the
sum of the lateral faces,
4(½ sl)
½ (4s)l
or ________=
________
Lateral Area of a Pyramid =
½ x perimeter of the base x slant
height
Surface Area of a Pyramid =
lateral area + area of the base
Example 2: The roof of a gazebo is a regular
octagonal pyramid with a base edge of 4
feet and a slant height of 6 feet. Find the
area of the roof.
Looking for the lateral area only.
1
1
L  pl  (32)(6)  96 ft 2
2
2
Example 3: A regular square pyramid has
base edges of 8 m and an altitude of 8 m.
Find the surface area and volume of the
pyramid.
8
Example 3: A regular square pyramid has
base edges of 8 m and an altitude of 8 m.
Find the surface area and volume of the
pyramid.
L
1
1
pl  (32)(4 5 )  64 5
2
2
8
4
S  L  B  64 5  64  64  64 5m 2
1
1
V  Bh  64  8  170. 6 m 3
3
3
8
4 2  82  c 2
c 2  80
c  80  4 5