1. A crash course in:
Three Dimensional Shapes Surface Area and Volume Formulas Platonic Solids

2. Parts of a polyhedra: faces edges vertices
Remember from last time
Today, we’re going to talk about specific polyhedra called:
Prisms
and
Pyramids

3. Bases
Lateral Faces
FACES can be either

4. PRISMS PYRAMIDS *have 1 base. *have 2 bases: they are || and 
*Lateral faces are ALWAYS triangles
*have 2 bases: they are || and 
*Lateral faces are ALWAYS rectangles or parallelograms

5. 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”
“trapezoidal”
“hexagonal”
Last name:
Names the family:
Prism Or
Pyramid

6. Volume Surface Area 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.

7. 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

8. Areas of Regular Polygons
What part of A=1/2bh 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

9. Let’s see how this works…10
A = 1/2ap
A = ½(6.88)(50)
A = 172 sq.units
6.88
PAINLESS!!
Let’s kick it up a notch…

10. Let’s find the area of this one
12 units
…and since we LOVE triangles, let’s start there.
60°
60°
60°
How many degrees would the central angle of each Δ have?
60°
60°
60°
30°
60°
Think of the center as a circle (360°) and divide
30°
60°
60°
Since the Δs are isosceles, what are the measures of the base angles?
60°
30°
60°
Since the apothem is an angle bisector, then what is the measure of the small top angle?
The short side = 6
The apothem = 6√3
A = 1/2ap
A = ½(6√3)(72) = 216√3 (exact)
A = (approx.)
6 units

11. 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°
72°
54°
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

12. Assignment
*Shape Identification Activity
* Area & Perimeter Wksht #1