Multi-Part Lesson 9-3 Composite Figures

Multi-Part Lesson9-3PARTMain IdeaFind the areas ofcomposite figures.glencoe.comComposite FiguresACBDArea of Composite Figures28 ftPOOLS The dimensions of apool at the recreation centerare shown.6 ft4 ft1. Describe the shape ofthe pool. See margin.14 ft2 ft2. How could youdetermine the area of "@/"@ "the pool’s floor? Separate the shape into a rectangle and a trapezoid,find the area of each, and add to find the total area.To find the area of a composite figure, separate it into figures withareas you know how to find. Then add those areas.Find the Area of a Composite FigureFind the area of the figure at the right.The figure can be separated into arectangle and a triangle. Find thearea of each.Area of Rectangle4 in.6 in.6 in.10 in.Area of Triangle4 in.6 in.4 in.10 in. "ART FILE: C11-14A NA 8740461A bhA bhA 10 · 6 or 60C09-110A-891639GlencoeCUSTOMER:2AlteredThebaseof theBY:triangle is MF1A (4)(4) or 8 10 - 6 or 4 inches.C09-111A-891639CS2EDITED BY:simpleonly altered@13greyscale2.5 cm12 ft1.5 cm9.2 cm31.4 cm2Lesson 9-3 Composite Figures " #4(pcomplexb.8 ft4 ft519 523 SE.indd 5192mod.blacklineFind the area of each figure.10 ftDATE:created@ NETSREVISION:60 ft29-19-2TIME: 8 mThe area is 60 8 or 68 square inches.a.JOB NUMBERDATE:5197/9/09 4:42:17 PMc

POOLS The diagram of the pool from the beginning of thelesson is shown below. Find the area of the pool’s floor.28 ft6 ft4 ft14 ft2 ftThe figure can be separatedinto a rectangle and a trapezoid. "@/"@ "The area of the rectangle is 28 14 or 392 square feet.1The area of the trapezoid is(2)(4 6) or 10 square feet.2So, the area of the pool’s floor is 392 10 or 402 square feet.Real-World LinkThe largest swimmingpool in the world islocated in Chile. It isone kilometer inlength and isequivalent toapproximately 6,000standard pools.Find the area of the figure at the right.The figure can be separated into asquare and a rectangle. The sharedrectangle, however, will be countedtwice if the areas are added, so thearea of the small rectangle, 6 7 or42, must be subtracted from the total.12 cm6 cm8 cm12 cm12 cm15 cmThe area of the square is 12 12 or 144 square centimeters.The area of the rectangle is 15 12 or 180 square centimeters.C09-103A-891639ART FILE: C11-14A NA 874046The sum of the areas is 144 180or 324 squarecentimeters.GlencoeCUSTOMER:TECHJOB NUMBER:Since the small rectangle was countedsubtract itsareaAltered BY:twice,MFDATE:CSfrom the total. 324 - 42 282 EDITED BY:DATE:So, the area of the figure is 282 square centimeters.c. DECKS Find the area of thedeck shown. 672 ft2only altered@ NETS1simple2mod.blackline34complexgreyscaled. Find the area of the figurebelow. 65 ft220 ft9-18-079-25-07TIME: 8 mcreated@ NETSREVISION:10555(place checkmark)( 4& .4 .B OE QBTT -,FMMv. complexcolor6 ft2 ft7 ft20 ft14 ft14 ft6 ft10 ft36 ft8 ft1 ftC12-181A-874046-A520Chapter 9 Use Formulas in GeometryC09-104A-891639519 523 SE.indd 5207/9/09 4:42:28 PM

Example 1(p. 519)Find the area of each figure. Round to the nearest tenth if necessary.112 m2 2.1.104.1 ft2 3.7m12 m6 ft4m4m6 ft15 m 4 m10 m15 ft14 m145 m210 mExamples 2 and 3(p. 520)4. APARTMENTS The manager of an apartment "complex will install new carpeting in a studio "apartment. The floor plan is shown at the right.What is the total area that needs to be carpeted?342.5 ft25. TILING The floor plan of a kitchen is shown atthe right. If the entire kitchen floor is to be tiled,how many square feet of tile are needed? 188 ft28 ft12 ft5 ft10 ftC11-125C-829633-A25 ft6 ft2 ft6 ft12 ft " "11 ft16 ft Step-by-Step Solutions begin on page R1.C11-133C-829633-BExtra Practice begins on page EP2.Example 1(p. 519)Find the area of each figure. Round to the nearest tenth if necessary.6.7 cm10 cm8 in.8 in.58.6 in2257.1 mm2 10.9.5 yd4 in.87.5 cm254.2 yd28.5.3 in.715 cm7 yd11.4 yd7 yd10 mm5.2 yd #20 mmExamples 2 and 3(p. 520)69.5 ft211.3 ft #8 ft4.3 ft12. BLUEPRINTS On a blueprint, " "a rectangular room14 feet by 12 feet has a semicircular sitting area #attachedwith a diameter of 12 feet. What is thetotal area of the room and the sitting area?about 224.5 ft213. POOLS The diagram at the right givesthe dimensions of a swimming pool. If acover is needed for the pool, what will bethe approximate area of the cover?592.83 ft2 #5.2 yd66.2 yd22 yd14 ft12 ft " "18 ft20 ft " "36 ftLesson 9-3 Composite Figures521C12-067A-874046-B519 523 SE.indd 5217/9/09 4:42:31 PM

14. GRAPHIC NOVEL Refer to the graphic novel frame below forExercises a–b.Let’s just findthe area of thelarger circleand take outthe area of thesmaller circle!a. Find the area of the dirt bike track. Use 3.14 for π. 3,061.5 ft2b. Suppose it costs 4.99 to cover one square foot of the dirt biketrack with dirt. How much will it cost to cover the track withdirt? Round to the nearest cent. 15,276.89B15 PAINTING The diagram shows one sideof a storage barn.a. This side needs to be painted. Findthe total area to be painted. 467.4 ft2b. Each gallon of paint costs 20 andcovers 350 square feet. Find the totalcost to paint this side once. Justifyyour answer. See margin.26.5 ft14.5 ft22.8 ft " "CHALLENGE Describe how to separate each state into simpler figures.Then use these figures to estimate the area of each state. One squareunit equals 2,400 square miles. Justify your answer.16. Sample answer:Add the areas of arectangle and atriangle. Area ofrectangle: 3 4 12; Area of triangle:1 3 3 4.5;16.Seemargin.17.NEVADA212 4.5 16.5. So,an approximate area18. C11-15A NA 874046-ADescribe how you would find9 cmis 16.5 2,400 ortheareaofthefigureshownattheright.Sample39,600 mi2.5 cmanswer: Separate it into a rectangle and a triangle, " find the area of each, and add.7 cm522Chapter 9 Use Formulas in Geometry "519 523 SE.indd 5227/9/09 4:42:35 PM

Practice19. What is the area of the windowshown? Use 3.14 for π. A20. The shaded part of the grid representsthe plans for a fish pond.48 in.If each square on the grid represents5 square feet, what is the approximatearea of the fish pond? G " "F. 175 square feetG. 165 square feet36 in.A. 2,236.68 in2H. 150 square feetC. 508.68 in2I. 33 square feetB. 1,728 in2D. 168 in2 " 21.EXTENDED RESPONSE To promote recycling, theground of the neighborhood playground shownsandboxis being covered by shredded tires. The sandbox will30 ftnot be covered.Part A What is the area, in square feet, of theshredded tire portion of the playground? 3,150 ft215 ft45 ft80 ftPart B If shredded tires cost 2.99 per square foot,at the required depth, how much will it cost to coverthe playground? 9,418.50 " Find the perimeter of each figure.22.25.8 in.4.3 in.4.3 in.4.3 in.4.3 in.4.3 in.4.3 in.23.(Lesson 9-3A)3 ft30 ft3 ft24.8 cm29.2 cm2.6 cm3 ft6.6 cm4 cm4 cm3 ft3 ft4 cmFind the area of each circle. Use 3.14 for π. Round to the nearesttenth.(Lesson 2225. radius 4.7 cm 69.4 cm26. radius 12 in. 452.2 in27. diameter 15 in. 176.6 in2Lesson 9-3 Composite Figures519 523 SE.indd 5235237/9/09 4:42:38 PM

find the area of each, and add to find the total area. To find the area of a composite figure, separate it into figures with areas you know how to find. Then add those areas. Find the Area of a Composite Figure Find the area of the figure at the right. 6 in. 4 in. 10 in. 6 in. " The figure can be separated into a rectangle and a triangle .