G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS

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1 G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit fo thei e. The tem egul efe to vey pecific type of hpe. It efe to the polygon tht h ll equl ide, ll equl ngle nd the mximum line of ymmety fo tht pticul numbe of ide. Regul polygon cn be incibed in cicle nd becue of thi we pply few new tem to thee polygon. Fit of ll, ech egul polygon h cente nd diu becue they e incibed in the cicle. The othe new tem i the pothem. The pothem i the pependicul ditnce fom the cente to ide of the egul polygon. In the equiltel, que nd hexgon the tingle tht e fomed by the diu, the pothem nd ide e ll pecil ight tingle. In the ce of the equiltel nd hexgon it i - ight tingle nd in the ce of the que 5-5 ight tingle i fomed. Thee tingle e vey impotnt in helping u detemine the e of thee egul polygon

2 G.GMD.1 STUDENT NOTES WS #5 The wy to viulize e of thee egul polygon i to clculte the e of conguent tingle inide them. We find the e of one tingle nd then multiply the e by 3 (3 tingle) in the ce of n equiltel o by 6 (6 tingle) in the ce of hexgon. Let do few exmple o you cn ee the tep. Given n equiltel with diu of 6 cm, detemine the e. If the diu i 6 cm, then the hot leg (pothem) i 3 cm nd the long leg (½ ide) i 3 3, thu mking the ide of the equiltel So to detemine the e it would be: Ae = 3( Ae of tingle) Ae = 3 ( be) ( height) Ae = 3 (6 3)( 3) Ae = 7 3 cm The kill lened elie when woking with pecil ight tingle come in vey hndy hee!! Given egul hexgon with ide of 8 cm, detemine the e. If the ide i 8 cm, then the hot leg (½ ide) i cm nd the long leg (pothem) i 3. So to detemine the e it would be: Ae = 6( Ae of tingle) 8 3 Ae Ae Ae = 6 ( be) ( height) = 6 (8)( 3) = 96 3 cm 3 8 Thee type of quetion vy concening wht the given infomtion i but they ll eot bck to the pecil ight tingle inide the equiltel tingle, the que o the egul hexgon. Two fomul tht povide hotcut fo e e deived when the ide length i given. Given the ide,, then the long leg i hlf of tht. The pothem i tht vlue divided by 3 which tionlize to the e: 3 6. Now we e edy to clculte 3 Ae = 3 ( ) 6 Ae = 3 cm 3 6

3 G.GMD.1 STUDENT NOTES WS #5 3 Given the ide,, then the hot leg i hlf of tht. The pothem i tht vlued multiplied 3 by 3 which i. Now we e edy to clculte the e: 3 Ae = 6 ( ) Ae = 3 3 cm 3 Inted of leving thee two fomul they e we could hve enged the infomtion to ummize them little diffeently. When we do thi we get nothe wy to think bout the e of egul polygon. Equiltel Fomul 3 Ae = 3 ( ) 6 3 Ae = 3( ) 6 1 Ae = ( peimete )( pothem ) Hexgon Fomul 3 Ae = 6 ( ) 6 3 Ae = 6( ) 6 1 Ae = ( peimete ) pothem ( ) AREAREGULAR POLYGON = 1 (peimete)(pothem) Fo ll of the othe egul polygon, tigonomety i needed becue the ngle within thei tingle e not the pecil one. Let me olve one of thee to demontte the tep. Given egul pentgon with ide length of 8 cm, detemine the e. When you divide the hpe into 5 conguent tingle we get 3/5 = 7 ngle. When dop the ltitude it cete the pothem 36 ight tingle i fomed. So uing tigonomety we cn detemine the pothem vlue. tn 36 = = tn 36 Now we cn detemine the e of the egul pentgon. A = (5 )( Ae of ) A = 5 (8) tn 36 A cm cm 7 7 cm

4 G.GMD.1 STUDENT NOTES WS #5 Find the AREA of ech egul polygon. Hexgon with diu 8 cm Sque with n pothem of 6 cm Equiltel tingle with diu 3cm 8 cm 3 cm 6 cm 3 cm 3 cm cm 6 cm 6 cm A = ½ p A = ½ ( 3)(8)(6) A = 96 3 cm A = ½ p A = ½ (6)()(1) A = 1 cm A = ½ p A = ½ ( 3)(1)(3) A = 36 3 cm

5 G.GMD.1 WORKSHEET #5 NAME: Peiod 1 1. Wht i the centl ngle of egul ) Octgon? b) Hexgon? c) Decgon? d) Tingle?. Find the pothem of ech egul polygon. ) Hexgon with ide of 15 cm EQUILATERAL b) Sque with digonl of 1 cm SQUARE c) Equiltel tingle with ide cm 5 3. Find the diu of ech egul polygon. ) Sque with ide 7 cm 5 5 HEXAGON b) Equiltel tingle with ide of 3 cm c) Hexgon with ide of 8 cm

6 G.GMD.1 WORKSHEET #5. Find the AREA of ech egul polygon. EQUILATERAL ) Sque with diu of16 cm b) Equiltel tingle with n pothem of cm c) Hexgon with peimete of 18 cm SQUARE d) Equiltel tingle with diu of 16 3cm 5 e) Regul Octgon with ide of 1 cm. 5 5 HEXAGON ( dec.)

7 G.GMD.I WORKSHEET #5 NAME: 1. Wht i the centl ngle of egul ei^o t te )Octon? 'tl -o b) Hexgon? U lo c) Decgon? 36' d)tingle?. Find th" jlf*tu-of ech egul polygon. l ) Hexgon with ide of 15 cm 7,{{A cttt (tl b)sque with digonl of lji cm G7.f c) Equiltel tingle with ide cm tli cu (E) # E'Y,!, q,li 3. Find ech egut potygon. ) Sque with ide 7 cm _(E) b) Equilteltingle with ide of ".6 cm '+ c,^t c) Hexgon with ide of 8 cm eg -, --= // t

8 G.GMD,7 WORKSHEET #5. Find th<pof ech egul polygon. ) Sque with diu ofllji cm *, /o7,1 cuxl ^Z 6? J L loz'{ b) Equilteltingle with n pothem of cm _(E),? c) Hexgon with peimete of 18 cm -T = 7 # x =Lo? = lq.,i\q) B'yl, ft.tf1 c^ G) d) Equilteltingle with diu of 16E cm GI'Y A e) Regul Octgon with ide of 1 cm. t /tt,tl 1{l t.,'yo- \ \ lzg VE=qE $,"' - (-,- fz'f =! g* = Tz.; $-= tl+'qt g It. ( dec.) A = L-? =,(^.wz' )()(-)

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