polygons. a polygon is a closed figure made by joining line segments, where each line segment...
TRANSCRIPT
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Polygons
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Polygons
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
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Polygons
Which are polygons?
1.
2.
3.
4.
5.
6.
7.
8.
9.
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Regular Polygons
A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.
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Regular Polygons
Why is a square considered a regular polygon?
Name another shape that you see almost everyday that is a regular polygon.
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Common Polygons
Triangles
Quadrilaterals
Pentagon
Hexagon
Octagon
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Triangles
A triangle having all three sides of equal length. The angles of an equilateral triangle all measure 60 degrees.
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Kinds of Triangles
•Equilateral
•Isosceles
•Scalene NO Sides Equal
All Sides Equal
2 Sides Equal
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Kinds of Triangles
•Acute
•Obtuse
•Right
All angles less than 90o
Has one angle greater than 90o but less than 180o
One angle = 90o
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Kinds of Triangles
•Acute
•Obtuse
•Right
All angles less than 90o
Has one angle greater than 90o but less than 180o
One angle = 90o
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Quadrilaterals
A quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals.
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Quadrilaterals
The five most common types are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus.
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Parallelogram
A parallelogram is a quadrilateral with opposite sides parallel.
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Rectangle
A rectangle is a quadrilateral with four 90-degree angles.
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Square
A square is a quadrilateral with four equal sides and four 90 degree angles.
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Trapezoid
A trapezoid is a quadrilateral that has two sides parallel
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Rhombus
A rhombus is a parallelogram with four equal sides.
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PENTAGON
A five-sided polygon.
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Hexagon
A six-sided polygon.
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Octagon
An eight-sided polygon.
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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.
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Perimeter
5
11
9
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Perimeter
3
8
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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.
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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.
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Area
You can find an area by drawing a shape on graph paper, and counting the squares inside the shape.
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Area
But this is not very practical…
Most polygons can be described as having a base and height.
hh
h
b bb
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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
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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
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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
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Triangle
Look at this rectangle:
Now, what do you have?
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Triangle
2 triangles from one rectangle.
Formula to find the area of a rectangle is A = b • h
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Triangle
What is formula for the area of ONE triangle?
A = ½ b • h
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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.
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Polyhedra
A polyhedra is simply a three-dimensional solid which consists of a collection of polygons, usually joined at their edges.
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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.
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PolygonPoly GonPenta 5 sidesHexa 6 sidesHepta 7 sidesOcta 8 sidesDeca 10 sides
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PolyhedraPoly HedraTetra 4 facesHexa 6 facesOcta 8 facesDeca 10 faces
Dodeca 12 faces
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Polygon
Polygon sides angles vertices
Triangle 5Quadrilateral 6
Pentagon 5Hexagon 6Heptagon 7Octagon 8Decagon 10