The Geometry Of Your Life (Part Two)

PyramidsThe Secret Of

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 pyramidA 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

Apex

Base

Lateral Faces

Height

Slant Length

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…

3 m3 m

5 m

3 m

3 m

5 m

Area= Square Area+ 4* Triangle Area=32+4*3*5/2=39 m2

An Easy Problem

3 m3 m

3 m

3 m

Area= Square Area+ 4* Triangle Area =32+4*3*?/2

A little more difficult …

4 m

Slant length?

Maybe you need to apply some famous theorem

Volume of a Pyramid• This is the formula to calculate the volume of a pyramid…

• But… why? This is the question…

heightareabase31

V

Manipulate

Maybe this picture is the key to solve this affair, hum… Très intéressant mon Dieu!

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.

Truncated Pyramids

Now you are ready to

identify every pyramid in your

life