Polygons

Polygons

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Polygons

Which are polygons?

1.

2.

3.

4.

5.

6.

7.

8.

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

•Isosceles

•Scalene NO Sides Equal

All Sides Equal

2 Sides Equal

Kinds of Triangles

•Acute

•Obtuse

•Right

All angles less than 90o

Has one angle greater than 90o but less than 180o

One angle = 90o

Kinds of Triangles

•Acute

•Obtuse

•Right

All angles less than 90o

Has one angle greater than 90o but less than 180o

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

11

9

Perimeter

3

8

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.

hh

h

b bb

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.

A = b • h

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

A = s2

h

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 = ½ b • 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.

PolygonPoly GonPenta 5 sidesHexa 6 sidesHepta 7 sidesOcta 8 sidesDeca 10 sides

PolyhedraPoly HedraTetra 4 facesHexa 6 facesOcta 8 facesDeca 10 faces

Dodeca 12 faces

Polygon

Polygon sides angles vertices

Triangle 5Quadrilateral 6

Pentagon 5Hexagon 6Heptagon 7Octagon 8Decagon 10