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Презентация на тему Pyramids; The Lateral Area of a Regular Pyramid (11th grade)

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PyramidsThe diagram shows the pentagonal pyramid V-ABCDE. Point V is the vertex home PyramidsThe five triangular faces with V in common, such as ΔVAB, are Most of the pyramids you'll study  will be regular pyramids. All Example 1A regular square pyramid has base edges 10 and lateral edges home Example 2Find the lateral area of the pyramid given in Example 1. home The Lateral Area of a Regular Pyramid  The lateral area of home The Volume of a Pyramidhome home The Volume of a PyramidhomeThe volume of a pyramid equals one third home Example 3homeSuppose the regular hexagonal pyramid shown has base edges 6 and home Example 4homeA regular triangular pyramid has lateral edge 10 and height 6. home Example 5homeThe shaded pyramid in the diagram is cut from a rectangular home
Слайды презентации

Слайд 2 home

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Слайд 3 Pyramids
The five triangular faces with V in common,

PyramidsThe five triangular faces with V in common, such as ΔVAB,

such as ΔVAB, are lateral faces. These faces intersect

in segments called lateral edges.

The height of a lateral face is called the slant height, l of the pyramid.

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Слайд 4 Most of the pyramids you'll study will be

Most of the pyramids you'll study will be regular pyramids. All

regular pyramids.
All lateral faces are congruent isosceles triangles.

The altitude meets the base at its center, O.

These are pyramids with the following properties:
The base is a regular polygon

All lateral edges are congruent

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Слайд 6 Example 1
A regular square pyramid has base edges

Example 1A regular square pyramid has base edges 10 and lateral

10 and lateral edges 13. Find its
slant height
height.


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Слайд 8 Example 2
Find the lateral area of the pyramid

Example 2Find the lateral area of the pyramid given in Example 1. home

given in Example 1.
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Слайд 9 The Lateral Area of a Regular Pyramid

The Lateral Area of a Regular Pyramid The lateral area of

The lateral area of a regular pyramid with n

lateral faces is

(the area of one lateral face x n)

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Слайд 11 The Volume of a Pyramid
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The Volume of a Pyramidhome

Слайд 13 The Volume of a Pyramid
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The volume of a

The Volume of a PyramidhomeThe volume of a pyramid equals one

pyramid equals one third the area of the base

times the height of the pyramid.

Слайд 15 Example 3
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Suppose the regular hexagonal pyramid shown has

Example 3homeSuppose the regular hexagonal pyramid shown has base edges 6

base edges 6 and height 12. Find its volume.


Слайд 17 Example 4
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A regular triangular pyramid has lateral edge

Example 4homeA regular triangular pyramid has lateral edge 10 and height

10 and height 6. Find the
(a) lateral area

(b) volume.

Слайд 19 Example 5
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The shaded pyramid in the diagram is

Example 5homeThe shaded pyramid in the diagram is cut from a

cut from a rectangular solid. How does the volume

of the pyramid compare with the volume of the rectangular solid?

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