Polygons
Polygons
A polygon is a closed figure
made by joining line segments,
where each line segment
intersects exactly two others.
Polygons
7.
Which are polygons?
2.
6.
1.
5.
4.
8.
3.
9.
Regular Polygons
A regular polygon is a polygon
whose sides are all the same
length, and whose angles are
all the same.
Regular Polygons
Why is a square considered a
regular polygon?
Name another shape that you
see almost everyday that is a
regular polygon.
Common Polygons
Triangles
Quadrilaterals
Pentagon
Hexagon
Octagon
Triangles
A triangle having all three sides
of equal length. The angles of
an equilateral triangle all
measure 60 degrees.
Kinds of Triangles
•Equilateral
All Sides Equal
•Isosceles
2 Sides Equal
•Scalene
NO Sides Equal
Kinds of Triangles
•Acute
All angles less than 90o
•Obtuse
Has one angle greater
than 90o but less than 180o
•Right
One angle = 90o
Kinds of Triangles
•Acute
All angles less than 90o
•Obtuse
Has one angle greater
than 90o but less than 180o
•Right
One angle = 90o
Quadrilaterals
A quadrilateral is a four-sided
polygon with four angles. There
are many kinds of
quadrilaterals.
Quadrilaterals
The five most common types
are the parallelogram, the
rectangle, the square, the
trapezoid, and the rhombus.
Parallelogram
A parallelogram is a
quadrilateral with opposite
sides parallel.
Rectangle
A rectangle is a quadrilateral
with four 90-degree angles.
Square
A square is a quadrilateral with
four equal sides and four 90
degree angles.
Trapezoid
A trapezoid is a quadrilateral
that has two sides parallel
Rhombus
A rhombus is a parallelogram
with four equal sides.
PENTAGON
A five-sided polygon.
Hexagon
A six-sided polygon.
Octagon
An eight-sided polygon.
Perimeter
The perimeter of a polygon is the
distance around the outside of the
polygon.
To find the perimeter of a polygon, take
the sum of the length of each side.
Perimeter
5
9
11
Perimeter
8
3
Perimeter
Find the perimeter of a square with each
side measuring 2 inches.
Find the perimeter of an equilateral triangle
with each side measuring 4 centimeters.
Find the perimeter of a regular pentagon
with each side measuring 3 inches.
Area
The area of a shape is a number that
tells how many square units are
needed to cover the shape.
Area can be measured in different
units, such as square feet, square
meters, or square inches.
Area
You can find an area by drawing a
shape on graph paper, and counting
the squares inside the shape.
Area
But this is not very practical…
Most polygons can be described as
having a base and height.
h
h
h
b
b
b
Rectangle
The area of a rectangle is equal to the
product of the length of its base and the
length of its height.
The height is a segment that is
perpendicular to the base.
h
A=b•h
b
Square
The square is a special rectangle, and you
can find its area using the rectangle
formula. The area of a square is equal to
the length of one side squared.
A = b2
A = h2
h
A = s2
b
Parallelogram
To find the area of a parallelogram, we use
the same formula that we used for the area
of a rectangle, multiplying the length of the
base times the length of the height.
A= b• h
h
b
Triangle
Look at this rectangle:
Now, what do you have?
Triangle
2 triangles from one rectangle.
Formula to find the area of a rectangle is A = b • h
Triangle
What is formula for the area of ONE
triangle?
A=½b•h
2-D & 3-D
Non Euclidian geometry, is the study of 2-D
and 3-D shapes.
A three-dimensional solid consists of a
collection of polygons, usually joined at their
edges.
Polyhedra
A polyhedra is simply a three-dimensional
solid which consists of a collection of
polygons, usually joined at their edges.
Polygon vs Polyhedra
The words are derived from the Greek word
poly (many) and gon (side) or hedra (face) .
A polyhedra is a 3-D shape with many
faces.
A polygon is a 2-D shape with many sides.
Polygon
Poly
Penta
Hexa
Hepta
Octa
Deca
Gon
5 sides
6 sides
7 sides
8 sides
10 sides
Polyhedra
Poly
Tetra
Hexa
Octa
Deca
Dodeca
Hedra
4 faces
6 faces
8 faces
10 faces
12 faces
Polygon
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Decagon
sides angles
5
6
5
6
7
8
10
vertices