11.3 perimeters and areas of similar figures

11.3 Perimeters and Areas of Similar Polygons Geometry

Objectives/Assignment ,[object Object],[object Object],[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

11.3 perimeters and areas of similar figures

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