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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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12.2pyramids

• 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.

• 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.

2 methods for finding the lateral area of a regular pyramid with the following properties

• Method 1

• Find the area of one lateral face and multiply by n (number of faces)

• Method 2 with the following properties

• 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. with the following properties

Find the L.A. with the following properties

• Hint, need to find slant height

• Probably going to need to find

the apothem of the base.

Volume with the following properties

• 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 with the following propertiesvolume

• 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. we need to determine using things like special right triangles, apothems, trigonometry, isosceles triangles, etc.485 1-10, 16, 18, 21, 23, 27