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