6-1b exploring polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · the sides are not...
TRANSCRIPT
![Page 1: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/1.jpg)
6-1B Exploring Polygons
How are polygons classified?
![Page 2: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/2.jpg)
You measured one-dimensional figures.
• Identify and name polygons.
![Page 3: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/3.jpg)
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.
![Page 4: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/4.jpg)
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.
![Page 5: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/5.jpg)
Definition
A convex polygon is one in which each
diagonal (except its endpoints) is in the
interior (inside) of the polygon.
![Page 6: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/6.jpg)
Convex Polygons
![Page 7: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/7.jpg)
Definition
A concave polygon is one in which at
least one diagonal (except its endpoints) is
not in the interior of the polygon.
Opps…
![Page 8: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/8.jpg)
Concave Polygons
![Page 9: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/9.jpg)
Not Polygons
![Page 10: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/10.jpg)
Definition
An Equilateral polygon is a polygon in
which all sides are congruent.
![Page 11: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/11.jpg)
Definition An Equiangular Polygon is a polygon in
which all angles are congruent.
![Page 12: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/12.jpg)
Definition
A regular polygon is a polygon that is
both equilateral and equiangular.
An irregular polygon is a polygon that is
not regular
![Page 13: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/13.jpg)
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
![Page 14: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/14.jpg)
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
![Page 15: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/15.jpg)
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
![Page 16: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/16.jpg)
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
![Page 17: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/17.jpg)
Area and Perimeter 1.6
What does the area of a figure
measure?
What does the perimeter of a figure
measure?
![Page 18: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/18.jpg)
• Identify and name polygons.
• Find perimeter, circumference, and area of two-dimensional figures.
![Page 19: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/19.jpg)
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.)
![Page 20: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/20.jpg)
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
![Page 21: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/21.jpg)
![Page 22: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/22.jpg)
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
![Page 23: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/23.jpg)
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
![Page 24: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/24.jpg)
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
![Page 25: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/25.jpg)
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
![Page 26: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/26.jpg)
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.
![Page 27: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/27.jpg)
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.
![Page 28: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/28.jpg)
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.
![Page 29: 6-1B Exploring Polygonsmrsdavisteachesmath.weebly.com/uploads/6/1/0/9/... · The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular . Name and Classify](https://reader033.vdocuments.us/reader033/viewer/2022050412/5f88dda4f8d2205f73367b7b/html5/thumbnails/29.jpg)
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