# Lesson 8.1 Areas of Rectangles and Parallelograms

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1 Leon 8.1 e of Rectngle nd Pllelogm 1. Find the e of the hded egion.. Find the e of the hded egion. 17 cm 9 cm 5 cm 8 cm 1.5 cm 13 cm cm cm 3. Rectngle D h e 684 m nd width 44 m. Find it length. 4. Find. 5. The ectngle nd the que hve equl e. The ectngle i 1 ft b 1 ft 4 in. 15 cm Wht i the peimete of the entie hegon in feet? 6 cm 39 cm 6. Dw pllelogm with e 85 cm nd n ngle with meue 40. I ou pllelogm unique? If not, dw diffeent one. 7. Find the e of PQRS. 8. Find the e of DEF. S( 4, 5) P( 4, 3) R(7, 1) (4, ) F (15, 7)E (, ) D(1, 7) Q(7, 9) (4, 5) (, 5) 9. n ce i equl to 43,560 ft. 4-ce ectngul ptue h 50-foot ide tht i 40 feet fom the neet od. To the neet foot, wht i the ditnce fom the od to the f fence?. ection of lnd i que piece of lnd 1 mile on ide. How mn ce e in ection? (1 mile 580 feet) 11. Dn bu piece of cpet tht meue 0 que d. Will he be ble to completel cove ectngul floo tht meue 1 ft 6 in. b 16 ft 6 in.? Eplin wh o wh not. Dicoveing Geomet Pctice You Skill HPTER 8 49

2 Leon 8. e of Tingle, Tpezoid, nd Kite 1. Find the e of the hded egion.. D i pllelogm, DE i kite, 1 cm D 18 cm, nd E cm. Find the e of DE. 0 cm D 3. e 16 in.. b cm, 8 cm, nd cm. Find D. b 16 in. 9 in. 5. concve kite (dt) h digonl meuing 13 cm nd 19 cm. Wht i it e? 6. The hded e i wht fction of the 7. Eplin wh the e of thi tingle lge pllelogm? cnnot be gete thn 7. E D midegment of tingle divide the tingle into tingle nd tpezoid. If the oiginl tingle h e 64 in., wht i the e of the tpezoid? 9. TP i tngent to cicle M nd N. TP 16 cm. The diu of N i 7 cm nd the diu of M i. Find the e of NMPT. T P N M. Find the e of TRI. 11. Find the e of HEXGN. I (1, 1) E (4, 6) X (7, 4) (0, 6) R ( 1, 3) H T (6, 0) (0, 1) N G (3, ) (7, ) 50 HPTER 8 Dicoveing Geomet Pctice You Skill

3 Leon 8.3 e Poblem 1. bundle of hdwood flooing contin 14 1 ft nd cot \$ How much will it cot to bu flooing fo the kitchen nd fmil oom? You hould bu 5% et to ccount fo wte.. Fo Wold Pece D celebtion the tudent t bot Junio/Senio High School e mking 6-m-b-8-m flg. Ech of the i gde will cete motif to hono the people of the i inhbited continent. Sketch thee poible w to divide the flg: one into i conguent tingle; one into i tingle with equl e but none conguent; nd one into i conguent tpezoid. Give meuement o mking on ou ketche o ech cl know it h equl e. 3. Olive h evolutionized the pizz indut b intoducing que pizz. She need to chge \$8.40 to ecove he cot on 1-inch (on ide) pizz. She then dd 5% nd ound up to the net multiple of qute. With thi picing cheme, wht hould Olive chge fo 16-inch pizz? 3 ft 13 ft 7 ft 3 ft 4 ft 18 ft Tile 18 ft Fieplce nd heth 4 ft Kitchen Fmil oom 6 ft 14 ft 4. et igtime ke h bked the wold lget chocolte cke. It i 600 cm b 400 cm b 180 cm high. et wnt to ppl foting to the fou ide nd the top. How mn lite of foting doe he need if 1 lite of foting cove bout 100 cm? 5. Jeome i mking mll metl kite pin to ell t the chool fi. Ech kite h n e of nd one digonl of 8 cm, which i divided b the othe digonl into cm nd 6 cm pt. The heet metl come in 7-cm-b-4-cm ectngle. How mn kite pin cn Jeome cut fom one heet? Wht pecentge of wte doe he hve? Dw cutting ptten Jeome could ue. 6. Kit nd Kt e building kite fo the big kite fetivl. Kit h led cut hi tick fo the digonl. He wnt to poition P o tht he will hve mimum kite e. He k Kt fo dvice. Wht hould Kt tell him? P Dicoveing Geomet Pctice You Skill HPTER 8 51

4 Leon 8.4 e of Regul Polgon In Eecie 1 3, the polgon e egul cm nd. 4. cm nd 3. 6 cm nd 14.5 cm. 197 cm cm. p 1-gon 4. In egul n-gon, 4.8 cm, 7., nd cm. Find n. 5. egul hegon with ide 8 cm h n e of ppoimtel 166 cm. Wht e the dimete of the incibed nd the cicumcibed cicle? In Eecie 6 8, dw ech egul polgon o tht it h peimete 0 cm. Ue the Regul Polgon e onjectue nd centimete ule to find the ppoimte e of ech polgon. 6. Pentgon 7. Octgon 8. Decgon 9. Ue comp nd tightedge to contuct egul octgon nd it pothem. Ue centimete ule to meue it ide length nd pothem nd the Regul Polgon e onjectue to find it ppoimte e.. Find the e of the hded egion between the que nd the egul octgon. 5 cm. 3 cm. 11. op the 3.6 /3 6 teelltion below howing the polgon ound ech tpe of vete. egul hegon with 3 cm h.60 cm. n equiltel tingle with 3 cm h 0.87 cm. If ech ide in thi teelltion i 3 cm, find the ppoimte e of ech dul polgon. 5 HPTER 8 Dicoveing Geomet Pctice You Skill

5 Leon 8.5 e of icle In Eecie 1 3, leve ou nwe in tem of. 1. If d 6.,.. If 59 cm,. 3. If 36 cm,. In Eecie 4 11, ound ou nwe to the neet 0.01 unit. 4. If 7.8 cm,. 5. If ,. 6. If d 3.1,. Fo Eecie 7 nd 8, efe to the figue of cicle incibed in n equiltel tingle. 7. Find the e of the 8. Find the e of the incibed cicle. hded egion nd 1 e tngent line. D i que. Find the e of the hded egion. 1 (, 7) D (6, 1). hoe i tetheed on 0 ft ope. If the ope i lengthened to 5 ft, b wht pecentge doe the hoe gzing e incee? 11. The thee cicle e tngent. Find the e of the hded egion. 5 cm 1. unning tck i hped like ectngle with emicicle on ech of the hote ide. The ditnce ound the tck i 1 mile (580 ft). The tightw i twice long the width of the field. Wht i the e of the field encloed b the tck to the neet que foot? Width Stightw Field Dicoveing Geomet Pctice You Skill HPTER 8 53

6 Leon 8.6 n W You Slice It In Eecie 1 6, find the e of the hded egion. Round ou nwe to the neet 0.01 cm cm 3 cm cm, 6 cm, 6. nd 3 9 cm. 8 cm 1 cm cm Shded e i 0 cm. 8. Shded e i 1. Find 9. Shded e i 15 cm. Find. to the neet 0.01 cm. Find OT to the neet 0.01 cm. 144 S T Q O. Rul dog, Spot, i tied with 0 ft ope to the cente of the bck wll of the hed. See the digm below. Ove wht e cn Spot pl, to the neet que foot? U Shed 1 ft 0 ft 54 HPTER 8 Dicoveing Geomet Pctice You Skill

7 Leon 8.7 Sufce e In Eecie 1 7, find the ufce e of ech olid. ll qudiltel e ectngle, nd ll meuement e in centimete. Round ou nwe to the neet 0.1 cm. 1.. e i egul hegon. 3. 6, 5., nd l l oth be e que que hole in ound peg In ode to clculte the het lo of thi etunt, Kevin need to find the e of the ufce tht i epoed to the i. i emicicle. ll meuement e in feet. Round ou nwe to the neet 0.1 ft Il i building mueum dipl ce. The ide nd bottom will be plwood nd the top will be gl. Plwood come in 4-ft-b-8-ft heet. How mn heet of plwood will he need to bu? Eplin. Sketch cutting ptten tht will leve he with the lget ingle piece poible. 1_ ft 3 ft 3 ft 1 1_ ft ft Dicoveing Geomet Pctice You Skill HPTER 8 55

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