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# 1 2. 2 p y r a m i d s PowerPoint PPT Presentation

1 2. 2 p y r a m i d s. 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

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1 2. 2 p y r a m i d s

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## 12.2pyramids

### 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 the

lateral faces are called the

lateral edges.

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

• Base is a regular polygon

• All lateral edges are congruent

• All lateral faces are congruent isosceles triangles. The height of a lateral face is called the SLANT HEIGHT of the pyramid.

• 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.

• 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.