5.2 Perimeters And Areas Of Similar Figures

English5.2SSTATESTANDARDSSpanishPerimeters and Areasof Similar FiguresHow do changes in dimensions of similargeometric figures affect the perimeters and areas of the figures?MA.7.G.4.11ACTIVITY: Comparing Perimeters and AreasWork with a partner. Use pattern blocks to make a figure whose dimensionsare 2, 3, and 4 times larger than those of the original figure. Find theperimeter P and area A of each larger figure.a. Sample: Square1111P 4P 8P 12P 16A 1A 4A 9A 16b. Triangle111P 3P 6P P A BA 4BA A c. Rectangled. Parallelogram12112200Chapter 5111P 6P 4A 2A CSimilarity and Transformations

Spanish2ACTIVITY: Finding Patterns for PerimetersWork with a partner. Copy and complete the table for the perimeters ofthe figures in Activity 1. Describe the pattern.PerimetersFigureOriginal SideLengthsDouble SideLengthsTriple SideLengthsQuadrupleSide LengthsP 4P 8P 12P 16P 3P 6P 6P 43ACTIVITY: Finding Patterns for AreasWork with a partner. Copy and complete the table for the areas of thefigures in Activity 1. Describe the pattern.FigureAreasEnglishOriginalSide LengthsDouble SideLengthsTriple SideLengthsQuadrupleSide LengthsA 1A 4A 9A 16A BA 4BA 2A C4. IN YOUR OWN WORDS How do changes in dimensions of similargeometric figures affect the perimeters and areas of the figures?Use what you learned about perimeters and areas of similar figuresto complete Exercises 8 –11 on page 204.Section 5.2Perimeters and Areas of Similar Figures201

English5.2SpanishLessonLesson TutorialsPerimeters of Similar FiguresEIf two figures are similar, then the ratioof their perimeters is equal to the ratioof their corresponding side lengths.Perimeter of ABCPerimeter of DEFABDEBCEFACDF—— — — —EXAMPLE1BDFCAFinding Ratios of PerimetersFind the ratio (red to blue) of the perimeters of the similar rectangles.46Perimeter of red rectanglePerimeter of blue rectangle4623——— — —23The ratio of the perimeters is —.1. The height of Figure A is 9 feet. The height of a similar Figure B is15 feet. What is the ratio of the perimeter of A to the perimeter of B ?Areas of Similar FiguresEIf two figures are similar, then theratio of their areas is equal to thesquare of the ratio of theircorresponding side lengths.BDAArea of ABCArea of DEF( ) ( ) ( )Chapter 5Similarity and TransformationsCAB 2BC 2AC 2 — —DEEFDF—— —202F

EnglishSpanishEXAMPLE2Finding Ratios of AreasFind the ratio (red to blue) of the areasof the similar triangles.6( )()6 210Area of red triangleArea of blue triangle—— —3 29 —52510 —925The ratio of the areas is —.EXAMPLE3Real-Life ApplicationYou place a picture on a page of a photo album. The page and thepicture are similar rectangles.a. How many times greater is the area of the page than the areaof the picture?b. The area of the picture is 45 square inches. What is the areaof the page?a. Find the ratio of the area of the page to the area of the picture.(Area of pageArea of picture6 in.)length of page 2length of picture—— ——() ()8 24 2 16 — —639 —8 in.169The area of the page is — times greater than the areaof the picture.169b. Multiply the area of the picture by —. 16945 — 80The area of the page is 80 square inches.Exercises 4 –132. The base of Triangle P is 8 meters. The base of a similarTriangle Q is 7 meters. What is the ratio of the area of Pto the area of Q?3. In Example 3, the perimeter of the picture is 27 inches.What is the perimeter of the page?Section 5.2Perimeters and Areas of Similar Figures203

EnglishSpanishExercises5.2Help with Homework1. WRITING How are the perimeters of two similar figures related?2. WRITING How are the areas of two similar figures related?3. VOCABULARY Rectangle ABCD is similar toRectangle WXYZ. The area of ABCD is 30 square inches.What is the area of WXYZ ? Explain.ABDCADWZWXZY12ABWX— —12— —6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas.124.5.115866.7.914478. How does doubling the side lengths of a triangle affect its perimeter?9. How does tripling the side lengths of a triangle affect its perimeter?10. How does doubling the side lengths of a rectangle affect its area?11. How does quadrupling the side lengths of a rectangle affect its area?12. BASKETBALL The Orlando Magic’s court is similar to a playground court. Theratio of the corresponding side lengths is 10 : 7. What is the ratio of the areas?13. LAPTOP The ratio of the corresponding side lengths of two similar computerscreens is 13 : 15. The perimeter of the smaller screen is 39 inches. What is theperimeter of the larger screen?Triangle ABC is similar to Triangle DEF. Tell whether the statement is true or false.Explain your reasoning.Perimeter of ABCPerimeter of DEFABDE14. —— —204Chapter 5Similarity and TransformationsArea of ABCArea of DEFABDE15. —— —

EnglishSpanish21 in.16. FABRIC The cost of the fabric is 1.31.What would you expect to pay for asimilar piece of fabric that is 18 inchesby 42 inches?9 in.6 in.10 ft17. AMUSEMENT PARK A model of amerry-go-round has a base areaModelof about 450 square inches. Whatis the percent of increase of the basearea from the model to the actualmerry-go-round? Explain.450 in.218. CRITICAL THINKING The circumference of Circle K is π.The circumference of Circle L is 4π.a. What is the ratio of their circumferences? of theirradii? of their areas?Circle KCircle Lb. What do you notice?19. GEOMETRY Rhombus A is similar to Rhombus B.What is the ratio (A to B) of the correspondingside lengths?20.ABArea 36 cm2Area 64 cm2A triangle with an area of 10 square meters has a base of4 meters. A similar triangle has an area of 90 square meters. What is theheight of the larger triangle?Find the percent of change. Round to the nearest tenth of a percent,if necessary. (Section4.2)SECTION4.221. 24 feet to 30 feet22. 90 miles to 63 miles23. 150 liters to 86 liters24. MULTIPLE CHOICE A runner completes an 800-meter race in 2 minutes40 seconds. What is the runner’s speed? (Section3.1)SECTION3.1A 3 sec10 m—B 160 sec1m—Section 5.2MSFL7PE 0502.indd 205C 5m1 sec—D 10 m3 sec—Perimeters and Areas of Similar Figures20510/20/09 3:23:08 PM

perimeter P and area A of each larger fi gure. a. Sample: Square b. Triangle c. Rectangle d. Parallelogram 2 1 2 1 1 1 1 1 P 6 P 4 A 2 A C P 4 P 8 P 12 P 16 A 1 A 4 A 9 A 16 5.2. Section 5.2 Perimeters and Areas of Similar Figures 201 4. IN YOUR OWN WORDS How do changes in dimensions of similar