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 ______ of the pyramid.

Base edge and lateral edge are defined in the same way they were for prisms.

vertex

vertex

base

lateral edge

lateral face

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.

altitudeorheight

Slantheight

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 ______ and the slant height intersects the base edge at its ________.

center

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?

)481)(776(3

1 2V

33.885,548,96 ftV

Consider a regular square pyramid whose slant height is l and whose base edge is s.

The area of each triangle of the net is _______

The lateral area is the sum of the lateral faces,or ________= ________

½ s l

½ (4s)l4(½ sl)

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.

only. area lateral for the Looking

pl2

1L 296)6)(32(

2

1ft

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.

8

8

4

5480

80

842

222

c

c

c

plL2

1

BLS

564)54)(32(2

1

25646464564 m

36.1708643

1mBhV

3

1