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Perimeters and areas of composite figures

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A composite figure is a plane figure made up of simple ... area of a region is equal to the sum of the areas of its nonoverlapping parts. A = A1 A2 A3 ... – PowerPoint PPT presentation

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Title: Perimeters and areas of composite figures


1
Perimeters and areas of composite figures
  • A composite figure is a plane figure made up of
    simple shapes or a 3-dimensional figure made up
    of simple 3-dimensional figures.

2
Perimeter
  • The perimeter of a plane composite figure is the
    sum of the lengths of its sides

20 in.
12 in.
3
Be careful !!!
  • Can the perimeter of a composite figure be found
    by adding the perimeters of the shapes that
    compose it?
  • NO! NO! NO! because this would be counting the
    "internal sides" and they should not be counted
    at all.

4
Area congruence postulatePostulate 19
  • If 2 polygons are congruent, then they have the
    same area

5
Area addition postulatePostulate 20
  • The area of a region is equal to the sum of the
    areas of its nonoverlapping parts
  • A A1 A2 A3

A3
A2
A1
6
HINT
  • Sometimes a figure will need to be divided into
    parts in order to find the area. Look for parts
    of the figure that appear to be rectangles or
    triangles and draw dotted lines to indicate how
    the figure should be divided

7
  • The Area Congruence postulate and the Area
    Addition postulate make it possible to find the
    area of complex composite figures by breaking
    them down into simpler shapes and finding the
    area of each shape

8
Find Area and perimeter
7 ft
3 ft
6 ft
4 ft
5 ft
9
Areas of composite figures by subtracting
  • Find the area of the shaded region

10 in.
10 in.
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