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# 11.1 - a If two polygonal regions intersect only in edges...

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Chapter 11- Polygonal Regions and Their Areas 11-1 Polygonal Regions A) Triangular regions a. The union of a triangle and its interior B) Polygonal region a. Is a plane figure formed by fitting together a finite number of triangular regions, in a plane, such that if two of these intersect, their intersection is either a point The third example has a ‘hole’ in it. This allowed by the definition. C) Postulate 19 (The Area Postulate) a. To every polygonal region there corresponds a unique positive real number

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D) Area a. The area of a polygonal region is the number assigned to it by Postulate 19. The area of the region R is denoted by aR. It is pronounced area of R. i. When the book speaks of a region, it is speaking of a polygonal region E) Postulate 20 (The Congruence Postulate) a. If two triangles are congruent, then the triangular regions determined by them have the same area i. If , then F) Postulate 21 (The Area Addition Postulate)

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Unformatted text preview: a. If two polygonal regions intersect only in edges and vertices (or do not intersect at all), then the area of their union is the sum of their areas i. If , then (as long as their intersection of the regions and is contained in a finite number of segment. ii. If and are triangular regions and R is their union, then iii. We can determine the correct value of aR by cutting the region up into non-overlapping triangles, and counting each triangular region only once. G) Postulate 22 (The Unit Postulate) a. The area of a square region is the square of the length of its edge. H) Theorem 11-1 a. The area of a rectangle is the product of its base and its altitude i. Proof ii. What is the area of the whole figure? iii. What is the area of the two squares and two rectangles within the large shape? (A represents the area of each rectangle)...
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