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6-1B Exploring Polygons
How are polygons classified?
You measured one-dimensional figures.
• Identify and name polygons.
Definitions A polygon is a closed figure formed by a
finite number of coplanar segments called
sides such that
The sides that have a common endpoint
are noncollinear, and
Each side intersects exactly two other
sides, but only at their endpoints.
Definition
A vertex of a polygon is the vertex of
each angle in the polygon.
A polygon is named by the letters of its
vertices, written in order of consecutive
vertices.
Definition
A convex polygon is one in which each
diagonal (except its endpoints) is in the
interior (inside) of the polygon.
Convex Polygons
Definition
A concave polygon is one in which at
least one diagonal (except its endpoints) is
not in the interior of the polygon.
Opps…
Concave Polygons
Not Polygons
Definition
An Equilateral polygon is a polygon in
which all sides are congruent.
Definition An Equiangular Polygon is a polygon in
which all angles are congruent.
Definition
A regular polygon is a polygon that is
both equilateral and equiangular.
An irregular polygon is a polygon that is
not regular
Classification of Polygons 3 sides Triangle
4 sides Quadrilateral
5 sides Pentagon
6 sides Hexagon
7 sides Heptagon
8 sides Octagon
9 sides Nonagon
10 sides Decagon
12 sides Dodecagon
20 sides Icosagon
“n” sides n-gon See page 57 for chart
Name and Classify Polygons
A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex.
The sides are not congruent, so it is irregular.
Answer: quadrilateral, convex, irregular
Name and Classify Polygons B. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
There are 9 sides, so this is a nonagon.
Lines containing some of the sides will pass through the interior of the nonagon, so it is concave.
Since the polygon is concave, it must be irregular.
Answer: nonagon, concave, irregular
Assignment 1-6
Page 61, 1-5, 11-16
You should have three answers for
1-2, 11-16.
1. Name by the number of sides
2. Convex or concave
3. Regular or irregular
Area and Perimeter 1.6
What does the area of a figure
measure?
What does the perimeter of a figure
measure?
• Identify and name polygons.
• Find perimeter, circumference, and area of two-dimensional figures.
Definition
He put a fence on the perimeter of the
property.
Perimeter of a polygon—the sum of the
lengths of the sides of the polygon (add the
length of the sides).
Circumference of a circle is the distance
around the circle.
Perimeter and circumference are the distance
around the figure. It is measured in linear
units (like inches or centimeters.)
Definition He measured the room and then figured the
area of the floor for the new carpet.
Area: the number of square units needed to
cover the surface (in a plane region).
1 2 3 4
5 6 7 8
For every polygonal region, there is a
unique positive number called the
area of the region.
If two polygonal regions are congruent,
then they have equal areas.
Area Postulates
Theorems
The circumference of a circle is the product of π and its diameter d.
C = πd
The circumference of a circle is twice the product of π and its radius r
C = 2πr
The area of a circle is the product of π
and the square of its radius r.
A = π·r2
Find the Perimeter and Area
20
P = 80
A = 400
21
56
P = 154
A = 1176
3 in
6.2 cm
C ≈ 18.85
A ≈ 28.3
C ≈ 18.85
A ≈ 28.3
Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).
Perimeter and Area on the
Coordinate Plane
Step 1
By counting squares on the grid, we find that CD = 6
units and DE = 5 units. Use the Distance Formula,
to find AB, BC, and EA.
The perimeter of pentagon ABCDE is 5.7 + 4.1 + 6 + 5 + 4.2 or about 25 units.
Step 2
Divide the pentagon into two triangles and a rectangle.
Find the area of the triangles.
Area of Triangle 1
Area of a triangle
Substitute.
Simplify.
Substitute.
Simplify.
Area of Triangle 2
Find the area of the rectangle.
Area of a rectangle
Substitute.
Simplify.
The area of pentagon ABCDE is 9 + 2.5 + 30 or 41.5 square units.
Answer: The perimeter is about 25 units and the area is 41.5 sq. units.
What does the area of a figure measure?
The number of square units contained in a
plane region.
What does the perimeter of a figure
measure?
The distance around the figure.
Assignment 1-6 day 2
p. 62, 17-22, 34-36
You must show your equation with the numbers in it
along with the answer to get credit for the
problem.
Example: P = 2(3.2) + 2(2.1) = 10.6
A = (3.2)(2.1) = 6.72
NO WORK NO CREDIT
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