Three Dimensional Shapes Surface Area and Volume Formulas Platonic Solids

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Three Dimensional Shapes Surface Area and
Volume Formulas Platonic Solids
A crash course in
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Parts of a polyhedrafacesedgesvertices
Remember from last time
Today, were going to talk about specific
polyhedra called Prisms and Pyramids
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FACES can be either
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PRISMS
PYRAMIDS
have 1 base. Lateral faces are ALWAYS triangles

• have 2 bases they are and ?
• Lateral faces are ALWAYS rectangles or
  parallelograms

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Naming Prisms and Pyramids

• They have 3 names just like most of you

First name RIGHT straight up and down all
lateral sides are rectangles or OBLIQUE at
least one lateral side is a parallelogram
(slanted)
Middle name Names the shape of the
base triangular rectangular octagonal trap
ezoidal hexagonal
Last name Names the family Prism Or Pyramid
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Surface Area
Volume
The number of cubic units inside a shape. units3

• The number of square units on the surface of a
  shape.
• units2

You should have a paper that lists all the
formulas for surface area and volume for various
shapes.
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A regular polygon is one where all the sides have
the same length and all the angles are the same
measure.

Pentagon
Square
Hexagon
Triangle
Heptagon
Dodecagon
Octagon
Nonagon
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Areas of Regular Polygons
What part of A1/2bh is the perpendicular
bisector?
Can you find the area of a triangle?

• The perpendicular bisector of a triangle in a
  polygon is called an APOTHEM.
• The formula for the area of a regular polygon is
  
• A ½ap
• a is the length of the apothem
• p is the perimeter of the polygon

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Lets see how this works
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• A 1/2ap
• A ½(6.88)(50)
• A 172 sq.units

6.88
PAINLESS!! Lets kick it up a notch
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Lets find the area of this one
12 units
and since we LOVE triangles, lets start there.
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How many degrees would the central angle of each
? have?
60
60
60
60
60
60
Think of the center as a circle (360) and divide

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60
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Since the ?s are isosceles, what are the measures
of the base angles?
Since the apothem is an angle bisector, then what
is the measure of the small top angle?
The short side 6 The apothem 6v3 A 1/2ap
A ½(6v3)(72) 216v3 (exact) A 374.12
(approx.)
6 units
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The second one is always easier

• Find the area of this regular pentagon

• Find the central angle
• Chop it in half
• Find the base angles
• Find the apothem
• Find the area A ½ ap

72
8 units
36
54
72
36
36
a
5.5
36
5.5
54
54
a
A ½ (5.5)(8)(5) A 110 sq. units
5.5
54
4 units
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Assignment

• Shape Identification Activity
• Area Perimeter Wksht 1