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11.3 Perimeters and Areas of Similar Polygons Geometry
Objectives/Assignment ,[object Object],[object Object],[object Object]
Comparing Perimeter and Area ,[object Object]
Comparing Perimeter and Area ,[object Object]
Thm 11.5 – Areas of Similar Polygons ,[object Object]
Thm 11.5 continued Side length of Quad I Side length of Quad II = a b Area of Quad I Area of Quad II = a 2 b 2 I II ka kb Quad I  ~ Quad II
Ex. 1:  Finding Ratios of Similar Polygons ,[object Object],[object Object],[object Object],5 10
Ex. 1:  Solution ,[object Object],[object Object],[object Object],5 10
Ex. 1:  Solution ,[object Object],[object Object],5 10
Using perimeter and area in real life Ex. 2:  Using Areas of Similar Figures Because the ratio of the lengths of the sides of to rectangular pieces is 1:2, the ratio of the areas of the pieces of paper is 1 2 : 2 2   or, 1:4
Using perimeter and area in real life Ex. 2:  Using Areas of Similar Figures Because the cost of the paper should be a function of its area, the larger piece of paper should cost about 4 times as much, or $1.68.
Using perimeter and area in real life ,[object Object],Ex. 3:  Finding Perimeters and Areas of Similar Polygons
Using perimeter and area in real life ,[object Object],[object Object],Ex. 3:  Solution
Using perimeter and area in real life ,[object Object],Ex. 3:  Solution perimeter of ABCDEFGH perimeter of JKLMNPQR = a b  76 8(14.25) = 76 114 = 2 3
Using perimeter and area in real life ,[object Object],Ex. 3:  Solution 9 9A = 980.4  • 4 A = 3921.6 A    435.7 Write the proportion. Cross product property. Divide each side by 9. Use a calculator.  The area of the smaller octagon is about 435.7 square feet. A 980.4 = 4 9

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Perimeters and Areas of Similar Polygons

  • 1. 11.3 Perimeters and Areas of Similar Polygons Geometry
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Thm 11.5 continued Side length of Quad I Side length of Quad II = a b Area of Quad I Area of Quad II = a 2 b 2 I II ka kb Quad I ~ Quad II
  • 7.
  • 8.
  • 9.
  • 10. Using perimeter and area in real life Ex. 2: Using Areas of Similar Figures Because the ratio of the lengths of the sides of to rectangular pieces is 1:2, the ratio of the areas of the pieces of paper is 1 2 : 2 2 or, 1:4
  • 11. Using perimeter and area in real life Ex. 2: Using Areas of Similar Figures Because the cost of the paper should be a function of its area, the larger piece of paper should cost about 4 times as much, or $1.68.
  • 12.
  • 13.
  • 14.
  • 15.