10-3 & 10-4 : Areas of special quadrilaterals by 7xS3ef

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									      3.1b: Area and Perimeter
                   - Quadrilaterals and composite shapes




M(G&M)–10–6 Solves problems involving perimeter,
circumference, or area of two dimensional figures (including
composite figures) or surface area or volume of three

M(G&M)–10–7 Uses units of measure appropriately and consistently
when solving problems across content strands; makes conversions
within or across systems and makes decisions concerning an
appropriate degree of accuracy in problem situations involving
measurement in other GSEs. (State)
   Area of Parallelograms

     Base



     height



              Base



               Base (b) = One side of the parallelogram

               Height (h) = distance between the bases
                       (must be perpendicular)

Area of a Parallelogram = (b)(h)

                                            Why ?
             Base



            height



                     Base
What shape will it make when we cut off the triangle on the side
and put in on the other side?


     A rectangle with the area= (base)*(height)
How many square yards of carpeting are needed to
cover the family room, hallway, and bedroom?
Area if Triangles
      1
   A  bh
      2
                                        But
   *b= base of the triangle             Why ?
   *h = height of the triangle



   * Both are touching the 90 degree angle in
   the triangle
                            h        h




              b


It is half of a parallelogram with the same exact base and height
  Area if a Rhombus

          1
 Area =     d1d 2
          2
                            d1


    d1  one diagonal
                            d2


d 2  the second diagonal
Example




 A rhombus has an area of 50 square mm.
 If one diagonal has a length of 10 mm,
 How long is the other diagonal.
 Area of a Trapezoid               Base


   1
A  h(b1  b2 )                    Height
                                   (has to be perpendicular
   2                               to bases)


                                     Base (parallel side)

h  height (the distance between the bases)
b1  one of the bases (a parallel side)
b 2)  the other base (opposite parallel side
Example


   #1- Find the area   #2 - Find the area
M(G&M)–10–9 Solves problems on and off the coordinate plane involving
distance, midpoint, perpendicular and parallel lines, or slope.

                                                          Find the area

                                                  Use a geometric (area) approach
                                                  Instead of algebraic (slope, distance)
                  3         2
                                6 units                  Now you have a rectangle
                                                         With dimensions of 4 by 6.
                      1
                                                    Area rectangle  (4)(6)  24 units 2
                      4 units
                                                   To get the area of the original
                                                   triangle, subtract the new
        1                                          triangles from the overall
  A1  (2)(4)  4 u 2                             rectangle.
        2                                          This will leave you with the area
        1                                          of the original triangle.
  A 2  (2)(6)  6 u 2         AOriginal Triangle  Arectangle  Asmaller   triangles
        2
        1                                        24 - 14
  A 3  (2)(4)  4 u 2
        2                                        10 u 2
Now you try an example
Does it work with other shapes?
The end
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