10-3_Area of Parallelograms by dandanhuanghuang

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									                   10:3 Area of
                  Parallelograms
Objective: Find the area of parallelograms
and composite figures
Standard: G4.2 Carry out a procedure to find the area of
quadrilaterals, regular polygons, and composite figures.



   RELEVENCE: Area of parallelograms is used in construction and
   interior design.

   PRIOR LEARNING: Area of basic figures is learned in elementary school.
     Perimeter of Squares &
          Rectangles
 Square
                    EXAMPLE: Find the perimeter.
P   = 4s
 Rectangle
                                              20cm
 P = 2l + 2w
 P – Perimeter   14cm
                                    12cm
 s – side
 l – length
 w – width
  Area of Square & Rectangle
 Square
                      EXAMPLE: Find the area.
A   = s2
 Rectangle
                                          20cm
A = l ◦ w
 A – area     14cm
                                 12cm
 s – side
 l – length
 w – width
                 Base:
 ANY side of a parallelogram can be called
 a base

 For each base, there is a corresponding
 altitude
                Altitude:
A corresponding altitude is any segment
 perpendicular to the base

 Thelength of an altitude is called the
 height of the parallelogram
  Perimeter of Parallelograms:
 P=add all sides
                       EXAMPLE: Find the perimeter.
 (do not use height)

P   – perimeter                  14cm      20cm



                                 12cm
      Area of Parallelograms:
A   = bh
                  EXAMPLE: Find the area.


A  – area
 b – base                 14cm      20cm

 h - height
                         12cm
               Postulate:
 Thearea of a region is the sum of the
 areas of all of its non-overlapping parts.
                   Example 1:
 Find    the area of the figure.
            7 ft




  12 ft


                                    5 ft


                    17 ft
                   Example 2:
 Find   the area of the figure.
         9 cm
3 cm



                        7 cm
       9 cm
                               4 cm

                13 cm
          Example 3: Real-world
              Application
   Taylor’s grandparents
    are moving into a
    retirement home.                               Bedroom
                                              Bath    2
    Before they move in,            Bedroom
                                                        12 ft
                                                                17 ft
                                       1
    they want to recarpet   20 ft
                                              5 ft      Hall
    the two bedrooms                                 20 ft
    and hall. Find the               14 ft
    amount of carpeting
    needed to cover this
    floor space.
                   YOUR TURN:
      Find   the area of each figure.
1.      4mm                 2.                   15 in.

                                 6 in.

8mm                                                                5 in.
                   6mm
                                         6 in.                             2 in.
                                                          16 in.
          10mm
            A – B Pair Share
1.   Person “A” works the first problem while
     person “B” observes and coaches when
     necessary.
2.   When “A” finishes, “B” is to initial the
     problem to show agreement with the
     results.
3.   “A” and “B” switch roles and repeat steps
     1 and 2.
             EXIT TICKET
 Show   your work!

 Youmay use your notes but DO NOT help
 each other!

								
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