Advanced Geometry
Inductive Reasoning
Lesson 3

Examples
NO HOLES
NO CURVES
SIDES
CANNOT
OVERLAP
Named by: all vertices written in consecutive order

Convex extend the sides all extensions lie outside the figure
Concave
“caves in” extend the sides any extension crosses inside the figure

# of sides and angles
7
8
9
10 n
5
6
3
4
Names of Polygons
Name of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon n - gon

convex polygon all the sides are congruent and all angles are congruent

Examples: Name each polygon by its number of sides.
Then classify it as convex or concave and regular or irregular.
Pentagon convex regular

Perimeter – the sum of the lengths of the sides of a polygon
Area – the number of square units needed to cover a surface
ADD ALL SIDES
A
 lw

Circumference – the distance around a circle
C

2
 r A
Area
  r 2

Example:
Mr. Smith has a circular fence that encloses an area with a diameter of 12 feet. Using the same fence, he wants to create a square fence. What is the maximum side length of the square?

Example:
Find the perimeter of a square with an area of 30 square centimeters.

Example:
Find the circumference of a circle with an area of 36
 square units.

Example:
Find the length of each side of the polygon below if its perimeter is 20 units.

Definition: a solid with all flat surfaces that enclose a single region of space
•All flat surfaces are called faces.
•The line segments where the faces intersect are edges.
•The points where the edges intersect are
vertices.

The two bases are parallel AND congruent.
Named by: the shape of the bases
Triangular Prism Rectangular Prism Pentagonal
Prism
A regular prism has bases that are regular polygons.

one base
Named for: the base
Triangular
Pyramid
Rectangular
Pyramid
Hexagonal
Pyramid

Examples : Identify each solid. Name the bases, faces, edges, and vertices.
This picture is on page 62 in your textbook.
Bases –
Faces –
Edges –
Vertices –

Examples : Identify each solid. Name the bases, faces, edges, and vertices.
This picture is on page 61 in your textbook.
Bases –
Faces –
Edges –
Vertices –

The two bases are congruent, parallel circles.
one circular base
NOT polyhedra (polyhedrons)

Examples : Identify each solid. Name the bases, faces, edges, and vertices.
This picture is on page 62 in your textbook.
Bases –
Faces –
Edges –
Vertices –

Examples : Identify each solid. Name the bases, faces, edges, and vertices.
This picture is on page 61 in your textbook.
Bases –
Faces –
Edges –
Vertices –

P

Perimeter of thebase


Prisms
SA

Ph

2 B
V

Bh
Pyramids
SA

1
2
Pl

B

1
V Bh
3

Cylinders
SA

2
 rh

2
 r 2
 
2 V r h
Cones
SA
  rl
  r 2
V

1
3

2 r h

Examples: Find the surface area and volume of the square prism.

Examples: Find the surface area and volume of the square pyramid.
This picture is on page 62 in your textbook.

Examples: Find the surface area and volume of the square pyramid.