Transcript Area of a pyramid

The Geometry Of Your
Life
(Part Two)
Pyramids
Do you know…?
The origin of the term is
not entirely clear. The
word pyramid is thought
to be derived from the
Greek words “Pyramis”
(Wheat cake) and
“Pyramidos”. Egyptian
historians suggest that
the word comes from
the Greek roots “Pur”
(fire) and “Met”
(measure).
Math definition of a pyramid
A pyramid is a polyhedron formed by connecting a
polygonal base and a point (top vertex of the
pyramid). Two connectors (edges), a side of the
base and the top vertex form a triangle or lateral
face. Look at the examples:
Rectangular Pyramid
Hexagonal Pyramid
Triangular Pyramid
Elements
• The base. It is the polygon at the bottom of the
pyramid.
• The lateral faces. These are each of the triangles
that rise from the sides of the base to the top vertex
of the pyramid. They’re usually isosceles triangles.
• The apex. It is the top vertex of the pyramid, usually
located just above the center of the base.
• The pyramid’s height. It is the distance from the
center of the base to the top vertex of the pyramid.
• The slant lengths. These are each of the lateral
faces’ heights that connect the apex with the middle
point of a side of the base.
Fill in the gaps with an appropriate word or
expression
Lateral Faces
Apex
Height
Slant Length
Base
Do you know…?
The Louvre Pyramid is
35 meters long on the
base, which is a square,
and 20.6 meters high.
There are 673 panels of
transparent glass
divided in 603
rhomboids and 70
triangles. Its total
weight is 180 tones and
the slope is about 51º.
Investigate…
How long are the slant heights of the
Louvre Pyramid?
Some clues:
•Square Pyramid
•35 m long on the base.
•20.6 m high.
•Someone’s Theorem
Area of a pyramid
• The area of a pyramid is the sum of the
areas of the base and the lateral faces.
• Depending on the type of base and the
given information about the lateral faces,
the calculations may be easier or more
difficult.
• To calculate it, it can be useful to think
about the polyhedron in terms of its planes.
• Look at the example…
An Easy Problem
5m
3m
3m
5m
3m
3m
Area= Square Area+ 4* Triangle Area=32+4*3*5/2=39 m2
A little more difficult …
Slant length?
3m
3m
4m
3m
3m
Area=
Square
Area+to
4*apply
Triangle
Area
=32+4*3*?/2
Maybe
you need
some
famous
theorem
Volume of a Pyramid
• This is the formula to calculate the
volume of a pyramid…
1
V  base area  height
3
• But… why? This is the question…
Manipulate
Maybe this picture
is the key to solve
this affair, hum…
Très intéressant
mon Dieu!
Truncated Pyramids
Truncated Pyramids
• The part that is left when a pyramid is cut
by a plane parallel to the base and the
apical part is removed, is called a frustum.
• A truncated pyramid is said to be a frustum
formed from a pyramid.
Now you are
ready to
identify every
pyramid in your
life