Two- and Three-Dimensional Figures
Advanced Geometry
Inductive Reasoning
Lesson 3
Polygon
Named by: all vertices written in consecutive order
ExamplesNO HOLES
NO CURVES
SIDES CANNOT OVERLAP
Convex Concave
extend the sides
“caves in”
any extension crosses inside the figure
all extensions lie outside the figure
extend the sides
# of sides and angles
Name of Polygon
3456789
10n
Names of Polygons
trianglequadrilateral
pentagonhexagonheptagonoctagonnonagondecagonn - gon
Regular Polygon
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 and Area of a Rectangle
Perimeter – the sum of the lengths of
the sides of a polygon
Area – the number of square units
needed to cover a surfaceA lwADD ALL SIDES
Circumference and Area of a Circle
Area
2A r
Circumference – the distance around a circle
2C r
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.
Polyhedron 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.
PrismsThe two bases are parallel AND congruent.
A regular prism has bases that
are regular polygons.
Named by: the shape of the bases
Triangular Prism Rectangular Prism Pentagonal Prism
Pyramidsone 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 –
CylindersThe two bases are congruent, parallel circles.
NOT polyhedra (polyhedrons)
Conesone circular base
Spheres
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 –
Height vs. Slant Height
Surface Area and Volume
Prisms Pyramids
2SA Ph B
V Bh
1
2SA Pl B
1
3V Bh
P Perimeter of thebaseB areaof the Basel slant height
Surface Area and Volume
Cylinders Cones22 2SA rh r
2V r h
2SA rl r
21
3V 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.