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1.7 Find Perimeter, Circumference, and Area

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1.7 Find Perimeter, Circumference, and Area &IND 0ERIMETER #IRCUMFERENCE AND !REA 'OAL + &IND DIMENSIONS OF POLYGONS &/2-5,!3 &/2 0%2)-%4%2 0 !2%! ! !.$ 9OUR .OTES #)2#5-&%2%.#% # 3QUARE 2ECTANGLE SIDE LENGTH S LENGTH * AND WIDTH W 0 Ê{ÃÊ 0 ÊÓ*ÊzÓÜÊ ! Ê ÃÓÊ ! Ê *ÜÊ 4RIANGLE #IRCLE SIDE LENGTHS A B RADIUS R AND C BASE B # ÊÓ:ÀÊ AND HEIGHT H ! Ê :À ÓÊ 0 Ê >ÊzLÊzVÊ 0I : IS THE RATIO OF A £ ! ÊÊÊ]ÊÊÊL z Ê CIRCLEgS CIRCUMFERENCE TO Ó ITS DIAMETER %XAMPLE &IND THE PERIMETER AND AREA OF A RECTANGLE 4ENNIS 4HE IN BOUNDS PORTION OF A SINGLES TENNIS COURT IS SHOWN &IND ITS PERIMETER AND AREA 0ERIMETER !REA 0 * W ! *W ÊÇnÊ ÊÓÇÊ ÊÇnÊÊÓÇÊ ÊÓ£äÊ ÊÓ£äÈÊ 4HE PERIMETER IS ÊÓ£äÊ FT AND THE AREA IS ÊÓ£äÈÊ FT #HECKPOINT #OMPLETE THE FOLLOWING EXERCISE )N %XAMPLE THE WIDTH OF THE IN BOUNDS RECTANGLE INCREASES TO FEET FOR DOUBLES PLAY &IND THE PERIMETER AND AREA OF THE IN BOUNDS RECTANGLE ÊÊ«iÀiÌiÀ\ÊÓÓnÊvÌ]Ê>Ài>\ÊÓnänÊvÌÓ ,ESSON s 'EOMETRY .OTETAKING 'UIDE #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY 9OUR .OTES %XAMPLE &IND THE CIRCUMFERENCE AND AREA OF A CIRCLE !RCHERY 4HE SMALLEST CIRCLE ON AN /LYMPIC TARGET IS 4HE APPROXIMATIONS CENTIMETERS IN DIAMETER &IND THE APPROXIMATE AND ]zARE CIRCUMFERENCE AND AREA OF THE SMALLEST CIRCLE COMMONLY USED AS APPROXIMATIONS 3OLUTION FOR THE IRRATIONAL &IRST FIND THE RADIUS 4HE DIAMETER IS CENTIMETERS NUMBER : 5NLESS SO THE RADIUS IS ]zÊ£ÓÊ ÊÈÊ CENTIMETERS TOLD OTHERWISE USE FOR : 4HEN FIND THE CIRCUMFERENCE AND AREA 5SE FOR : 0 :R yzÊΰ£{Ê ÊÈÊ ÊÎÇ°ÈnÊVÊ ! :R yzÊΰ£{ÊÊÈÊ Ê££Î°ä{ÊVÓÊ #HECKPOINT &IND THE APPROXIMATE CIRCUMFERENCE AND AREA OF THE CIRCLE ÊÊ ÊyÊxä°Ó{ÊÆÊÊyÊÓää°ÈÊÓ %XAMPLE 5SING A COORDINATE PLANE 4RIANGLE *+, HAS VERTICES * + AND , &IND THE APPROXIMATE PERIMETER OF TRIANGLE *+, 3OLUTION &IRST DRAW TRIANGLE *+, IN A COORDINATE PLANE 4HEN FIND THE SIDE LENGTHS 7RITE DOWN YOUR ] CALCULATIONS TO "ECAUSE *+zIS HORIZONTAL USE THE Ê,ÕiÀÊ*ÃÌÕ>ÌiÊ TO FIND *+ 5SE MAKE SURE YOU DO NOT MAKE A MISTAKE THE Ê ÃÌ>ViÊÀÕ>Ê TO FIND SUBSTITUTING VALUES *, AND ,+ IN THE $ISTANCE &ORMULA *+ {ÊÈÊ Ê£Ê{zÊxÊ UNITS ]]] ] *, qÊÎÊ z z ÊÈÊ z qÊÓäÊÊÊzy Ê{°xÊ UNITS ]]] ] ,+ qÊÈÊ z ÊÈÊz z qÊÓxÊÊÊz ÊxÊ UNITS 4HEN FIND THE PERIMETER 0 *+ *, ,+ y ÊxÊ Ê{°xÊ ÊxÊ Ê£{°xÊ UNITS #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY ,ESSON s 'EOMETRY .OTETAKING 'UIDE 9OUR .OTES %XAMPLE 3OLVE A MULTI STEP PROBLEM ,AWN CARE 9OU ARE USING A ROLLER TO SMOOTH A LAWN 9OU CAN ROLL ABOUT SQUARE YARDS IN ONE MINUTE !BOUT HOW MANY MINUTES DOES IT TAKE TO ROLL A LAWN THAT IS FEET LONG AND FEET WIDE 3OLUTION 9OU CAN ROLL THE LAWN AT A RATE OF SQUARE YARDS PER MINUTE 3O THE AMOUNT OF TIME IT TAKES YOU TO ROLL THE LAWN DEPENDS ON ITS Ê>Ài>Ê 3TEP &IND THE AREA OF THE RECTANGULAR LAWN !REA *W Ê£ÓäÊÊÇxÊ ÊäääÊ FT 4HE ROLLING RATE IS IN SQUARE YARDS PER MINUTE 2EWRITE THE AREA OF THE LAWN IN SQUARE YARDS 4HERE ARE ÊÎÊ FEET IN YARD AND ÊÎÊ ÊÊ SQUARE FEET IN ONE SQUARE YARD YD FT + Ê£äääÊYD 5SE UNIT ANALYSIS FT 3TEP 7RITE A VERBAL MODEL TO REPRESENT THE SITUATION 4HEN WRITE AND SOLVE AN EQUATION BASED ON THE VERBAL MODEL ,ET T REPRESENT THE TOTAL TIME IN MINUTES NEEDED TO ROLL THE LAWN !REA OF LAWN 2OLLING RATE 4OTAL TIME ­YD® ­YD PER MIN® MIN Ê£äääÊÊzÊ£ÓxÊ + T 3UBSTITUTE ÊnÊÊzT $IVIDE EACH SIDE BY Ê£ÓxÊ )T TAKES ABOUT ÊnÊ MINUTES TO ROLL THE LAWN ,ESSON s 'EOMETRY .OTETAKING 'UIDE #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY 9OUR .OTES %XAMPLE &IND UNKNOWN LENGTH 4HE BASE OF A TRIANGLE IS FEET )TS AREA IS SQUARE FEET &IND THE HEIGHT OF THE TRIANGLE 3OLUTION £ ! Ê Ê]ÊÊÊL z Ê !REA OF A TRIANGLE Ó £ ÊÓ£ÈÊ ÊÊÊ]ÊÊÊ­Ó{®­z ®Ê 3UBSTITUTE Ó ÊÓ£ÈÊ Ê£Ó Ê -ULTIPLY Ê£nÊ H 3OLVE FOR H 4HE HEIGHT IS Ê£nÊ FEET #HECKPOINT #OMPLETE THE FOLLOWING EXERCISES &IND THE PERIMETER OF THE TRIANGLE SHOWN AT THE RIGHT ÊÊ>LÕÌʣǰ£ÊÕÌà 3UPPOSE A LAWN IS HALF AS LONG AND HALF AS WIDE AS THE LAWN IN %XAMPLE 7ILL IT TAKE HALF THE TIME TO ROLL THE LAWN %XPLAIN ]ÊÌÊÜÊÌ>iÊ>ʵÕ>ÀÌiÀÊvÊÌ iÊÌiÊÌÊÀÊÌ iÊ >ÜÊLiV>ÕÃiÊÌÊÃÊ>ʵÕ>ÀÌiÀÊvÊÌ iÊÀ}>Ê>Ài>° (OMEWORK 4HE AREA OF A TRIANGLE IS SQUARE INCHES AND ITS HEIGHT IS INCHES &IND THE LENGTH OF ITS BASE Ó{ÊV ià #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY ,ESSON s 'EOMETRY .OTETAKING 'UIDE .
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