12.2 pyramids

Names of pyramids

Names are based on the shape of the pyramids base. Reference whether it is regular or not

To label a pyramid you start with the vertex, and then a hyphen, and then list the vertices of the base.

This pyramid is a regular pentagonal pyramid

Referred to as V-ABCDE

V is the vertex ABCDE is the base

The segment from the vertex perpendicular to the base is the altitude.

The 5 faces that have V in common are the lateral faces. The edges of thelateral faces are called thelateral edges.

Most pyramids that you will encounter are regular pyramids, with the following properties

1. Base is a regular polygon2. All lateral edges are congruent3. All lateral faces are congruent

isosceles triangles. The height of a lateral face is called the SLANT HEIGHT of the pyramid.

4. The altitude meets the base at its center.

Slant height

2 methods for finding the lateral area of a regular pyramid

Method 1 Find the area of one lateral face and

multiply by n (number of faces)

Method 2 Theorem – the lateral area of a regular

pyramid equals half the perimeter of the base times the slant height (l).

L.A. = ½ Pl

Find the L.A.

Find the L.A. Hint, need to find slant height Probably going to need to find

the apothem of the base.

Volume

The volume of a pyramid equals one third the area of the base times the height of the pyramid. (V=1/3 Bh)

Tip – if the base is a regular polygon then you need to use the formula A= ½ aP to find the base area.

Find the volume Suppose this figure has base

edges of 8 and height of 12

Again the formulas may seem basic but there are values that we need to determine using things like special right triangles, apothems, trigonometry, isosceles triangles, etc.

“Mathematicians stand on each other's shoulders.”▪ Gauss

What one person has accomplished in mathematics is due to the many that came before them, this idea reverberates through concepts as well.

Pg. 485 1-10, 16, 18, 21, 23, 27