how do we find the area of parallelograms, kites and trapezoids?

How Do We Find The Area of Parallelograms, Kites and Trapezoids?

 

 

Trapezoid

a quadrilateral with exactly one pair of parallel sides

Area= (b1+b2)/2(h)

 

 

 

http://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid/picture-of-trapezoid.gif

 

 

 

 

Kites

two pairs of consecutive congruent sides

Area= d1d2/2

 

 

 

http://www.wyzant.com/Images/Help/trap_kite6.gif

 

 

 

 

 

 



how do we identify solids?

How Do We Identify Solids?

 

Solid Geometry

The geometry of 3 dimensional space

-3 dimensions (3D)- width, depth, and height

 

 

 

 

http://www.gotoandplay.it/_articles/2004/07/3dCube/cube.gif

 

 

Properties

Solids have properties such as:

-volume (think of how much water it could hold)

- surface area (thinks of the area you would have to paint)

 

Two types of solids, "polyhedral", and "non-polyhedral"

 

Polyhedra

They must have flat faces

 

Prism

Has the same cross section all along it's length

http://www.mathsteacher.com.au/year7/ch09_polygons/06_polyhedra/Image11220.gif

 

 

 

Pyramids

 

 

http://www.mathsisfun.com/geometry/images/pyramid-height-perimeter.jpg

 

 

Non- Polyhedra

Any surface that isn't flat

examples:

 

Sphere

 

http://etc.usf.edu/clipart/41700/41749/FC_Sphere_41749_lg.gif

 

 

 

 

 

Torus

 

 

 http://www.math.cornell.edu/~mec/2003-2004/geometry/torii/torus.jpg

 

 

Cylinders

 

http://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Circular_cylinder_rh.svg/220px-Circular_cylinder_rh.svg.png

 

 

 

 

 

Cone

 

http://accad.osu.edu/~pgerstma/class/vnv/resources/info/AnnotatedVrmlRef/Images/Cone.gif

 

 

Cross sections

The shape you get when cutting straight across an object

 

 

Surface Area

Area of the bases + lateral area (area of the sides)

 



 

 



How Do We Use Conjunctions and Disjunctions?

 

 

Conjunctions:

Hooking up words and phrases and clauses with AND.

- Has two statements connected by AND

 

 

Disjunctions:

Hooking up words and phrases and clauses with OR

- Has two statements connected by OR

 

 

Conditional:

The most frequently used statement in the construction or an argument or in the study of mathematics

       -Conditional- "if" (hypothesis), "then" (conclusion)

       - Inverse- Negate "if", "then"

       - Converse- switch "if", "then"

       - Contrapositive- Negate the converse 

How Do We Use Contrapositives?

 

Contrapositives:

Contra- prefix meaning "against" or "opposite"

you negate AND switch the hypothesis and conclusion (inverse and converse)

 

 

Examples:

1. "If I study, then I'll pass geometry." = "If I don't pass geometry, then I didn't study."

     2.  "If I am tired. then I will go to sleep." = "If I don't go to sleep, then I am not tired."

 

The "if" and "then" don't change with the hypothesis and the conclusion.

   

     3. "If Lisa sells the house, than her income will not remain the same." = "If her income does stay the same, then Lisa won't sell the house."

    

    4. "If a number is divisible by six, than it is divisible by three." = "If a number isn't divisible three, then it isn't divisible by six."