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21 Cards in this Set

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WHAT ARE THE FOUR CRITICAL WORDS OF COMP 19?
PARIMETER
AREA
VOLUME
CIRCUMFRANCE
P
A
V
C
FIRST OF THE THREE DISTRBUTERS FOR COMP 19)
USE AREA AND VOLUME FORMULAS TO SOLVE PROBLEMS
D1
SECOND OF THE THREE DISTRBUTERS FOR COMP 19)
USE PROPORTIONAL REASONING, WITH SIMILAR FIGURES
D2
THIRD OF THE THREE DISTRBUTERS FOR COMP 19)
RECOGNIZE A VARIETY OF TWO-DIMENSIONAL REPRESENTATIONS OF PARTS OF THREE DIMENSIONAL FIGURES
D3
FORMULAS: SEVERAL FORMULAS ON THE PAGE OF SBEC TEST BOOK: THE FOLLOWING FORMULAS ARE ONES YOU MAY NEED ARE NOT LISTED ON TEST BOOKLET-PERIMETERS
POLYGONS: ADD UP ALL SIDES
AREA:PARALLELOGRAM, RECTANGLE, SQUARE IS (BH OR BASE TIMES HEIGHT
KNOW THE FOLLOWING FORMULAS POLYGONS, PARRALLELGRAMS
VOLUME ALL NEED ARE PROVIDED ON TEXTBOOK?
TRUE
WHAT ARE THE PROPORTIONAL REASONING THAT WILL BE ON THE T TEST?
SIMILAR FIGURES
SCALED REPRESENTATIONS
AREA EFFECTS: THE RATIO OF CORROSPONDING ANGLE SIDES IS SQUARED TO GET THE RATIO OF CORROSPONDING ANGLES (2)
VOLUME EFFECTS: THE RATIO OF CORRESPONDING SIDES IS CUBED TO GET THE RATIO OF CORROSPONDING VOLUMES (3)
SCALED REPRESENTATIONS
AREA EFFECTS: THE RATIO OF CORROSPONDING ANGLE SIDES IS SQUARED TO GET THE RATIO OF CORROSPONDING ANGLES (2)
VOLUME EFFECTS: THE RAION OF CORRESPONDING SIDES IS CUBED TO GET THE RAIO OF CORROSPONDING VOLUMES (3)
WHAT ARE THE MULTIPLE REPRESENTATIONS TO SOLVE PROBLEM
Be able to use the following figures and theri formulas verbally, numericall, graphicaly and symbolically:
circles, triangles, cylinders, prism, sheres
verbally, numericall, graphicaly and symbolically:
circles, triangles, cylinders, prism, sheres
projections-what are they?
think of a movie theater here. When the movie is projeced on the screen, the size of tthe image depeonds on how foar the progector is frrom the screen, the sam thing for the overhead projector. this involves proportional reasoning
this subject involves proportional reasoning
what are cross sections
cross-sections-created when a passed horizontally or veritcally throuh a solid figure
volume=base * the surface of a three-dimensional figure height
v=bh
volume=? base X height
define nets:
these are patterns fo rconstrctting solid figurs. It is easer to determine the surface are of a thrree dimensional figure if you use a net
nets
cylindes formula
Pie X (radius)^2 X height
Cylinder
Volume = pr2 x height
V = pr2 h
Surface = 2p radius x height
S = 2prh + 2pr2
cylinder formula
sphere formula
Sphere
Volume = 4/3 pr3
V = 4/3 pr3
Surface = 4pr2
S = 4pr2
rectangle and perimenter
formulaRectangle:
Area = Length X Width
A = lw

Perimeter = 2 X Lengths + 2 X Widths
P = 2l + 2w
Rectangle:
Area = Length X Width
A = lw

Perimeter = 2 X Lengths + 2 X Widths
P = 2l + 2w
parallogram
Parallelogram
Area = Base X Height
a = bh
parallellelogram
trangle formula
Triangle
Area = 1/2 of the base X the height
a = 1/2 bh
Perimeter = a + b + c
(add the length of the three sides
triangle
circle formula
The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles.
d = 2r
c = pd = 2 pr
A = pr2
(p=3.14)
circle
prism formula
Prisms
Volume = Base X Height
v=bh
Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)
polygon formulas
polygon formulas Lesson Page
Math A
Sum of Interior Angles of a Polygon





A Polygon is a many sided figure. It has the same number of angles as sides.





The formula we use to find the sum of the interior angles of any polygon comes from the following idea:

Suppose you start with a pentagon. If you pick any vertex (the point where any 2 sides meet) of that figure, and connect it to all the other vertices, how many triangles can you form?


If you start with vertex A and connect it to all other vertices (it's already connected to B and E by sides) you form three triangles. Each triangle contains 1800. So the total number of degrees in the interior angles of a pentagon is:

3 1800 = 5400





Using the pentagon example, we can come up with a formula that works for all polygons. Notice that a pentagon has 5 sides, and that you can form 3 triangles by connecting the vertices. That's 2 less than the number of sides. It's the same principle for all polygons. If we represent the number of sides of a polygon as n, then the number of triangles you can form is (n-2). Since each triangle contains 1800, that gives us the formula:


Sum of Interior Angles
= 180(n-2)




Using the Formula

There are two types of problems in which we can use this formula:

1. Questions that ask you to find the number of degrees in
the sum of the interior angles of a polygon.
2. Questions that ask you to find the number of sides of a
polygon.

Hint: When working with the angle formulas for polygons, be sure to read each question carefully for clues as to which formula you will need to use to solve the problem. Look for the words that describe each formula, such as the words sum, interior, and angles.




Example 1: Find the number of degrees in the sum of the interior angles of an octagon.

An octagon has 8 sides. So n = 8. Using our formula from above, that gives us 180(8-2) = 180(6) = 10800.



Example 2: How many sides does a polygon have if the sum of its interior angles is 7200 ?

Since, this time, we know the number of degrees, we set the formula above equal to 7200, and solve for n.
180(n-2) = 720
n-2 = 4
n= 6
Set the formula = 7200
Divide both sides by 180
Add 2 to both sides



Names of Polygons

Listed below are some of the more common polygons whose names you should know:

Triangle 3 sides
Quadrilateral 4 sides
Pentagon 5 sides
Hexagon 6 sides
Heptagon or Septagon 7 sides
Octagon 8 sides
Nonagon or Novagon 9 sides
Decagon 10 sides
Dodecagon 12 sides
do example 2, 3 in text
do examples two and three on paper