2500 YEARS AGO A GREEK MATHEMATICAN NAMED PYTHAGORIS

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2500 YEARS AGO, A GREEK MATHEMATICAN NAMED PYTHAGORIS, SAID THAT IN A RIGHT TRIANGLE, THE SUMS OF THE SQUARES OF THE LENGTHS OF THE LEGS (A AND B) IS EQUAL TO THE SQUARE OF THE HYPOTENUSE.

IDENTIFYING THE TRIANGLE HYPOTENUSE IS ACROSS FROM THE RIGHT ANGLE LEG A LEG B

This is the formula a² b² a² + b² = c² c² ADD THE SQUARES OF A AND B TO GET THE SQUARE OF C !

IT’S PROBLEM TIME! WRITE FORMULA PLUG IN NUMBERS SOLVE 5 m c 12 m a² + b² = c² 5² + 12² = c² 25 + 144 = C² 169 = C 13 = C REMEMBER THE WARMUP SLIDE?

NOW YOU TRY ONE, AT YOUR DESK! A IS 12, B IS 16, AND THEY ARE LOOKING FOR THE HYPOTENUSE! 12 c 16

DID YOU GET IT RIGHT? C 12 a² + b² = c² 12² + 16² = c² 144 + 256 = c² 400 = c 20 = c 16 BE SURE TO WRITE THE FORMULA EACH TIME, PLUG IN THE NUMBERS AND SOLVE

WRITE THE FORMULA, PLUG IN THE NUMBERS, SQUARE, THEN ADD, THEN FIND THE SQUARE ROOT OF THE NUMBER. 3 C 4 a² + b² = c² 3² + 4² = c² 9 + 16 = c² 25 = c²

A 35 FOOT TELEPHONE POLE NEEDS A SUPPORT WIRE ATTACHED AT THE TOP OF THE POLE TO A POINT IN THE GROUND 20 FEET AWAY FROM THE BASE. ABOUT HOW LONG SHOULD THE WIRE BE? a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² 40. 3 or 40 ft = c C 20 35

Pythagorean Theorem – Day 2 x x

Try these on your own! x x

WORD PROBLEMS A 20 ft LADDER IS LEANED AGAINST A WALL. IF THE BASE IS 5 ft FROM THE WALL, HOW HIGH CAN YOU CLIMB? 20 ? 5 a² + b² = c² b = 375 5² + b² = 20² b = 19. 3 25 + b² = 400 19, 20 b² = 400 - 25 b² = 375 AS TOM SWAM ACROSS A 60 m RIVER, THE CURRENT MOVED HIM 20 m DOWNSTREAM. HOW FAR DID HE SWIM? 60 a² + b² = c² 60² + 20² = c² 3600 + 400² = c² 4000 = c² 20 4000 = c² 63. 2 = c² 64, 65

HOW FAR IS THE HELICOPTER FROM IT’S STARTING POINT? a² + b² = c² 6² + 9² = c² 36 + 81 = c² 117 = c² 9 mi 6 mi 117 = c² 10. 82 = c² A 35 ft LADDER IS LEANED AGAINST A BLDG. HOW HIGH IS THE WINDOW LEDGE ABOVE THE GROUND? b = 31. 6 35 ft ? 15 ft a² + b² = c² a² = 1000 a² + 15² = 35² a² = 1000 a + 225 = 1225 a = 31. 62 a² = 1225 - 225 31² = 961 and 32² = 1024

Missing Leg Wkst – EVENS ONLY! Use the scrambled answers to help you check your answers!

Extra Practice with Pythagorean Theorem 1) A small rectangular cabinet door has a width of 12 inches and a diagonal of 28 inches. Find the length of the door. 2) What is the AREA and PERIMETER of the door?

A BIG SCREEN T. V. IS 6 ft WIDE AND 11 ft LONG. HOW LONG IS THE DIAGONAL ACROSS THE SCREEN? 11 ? a² + b² = c² 6² + 11² = c² 36 + 121 = c² 157 = c² 6 157 = c 12. 53 = c KERSTIN LEFT HER CAMPSITE AND HIKED 5 mi EAST AND THEN 2 mi NORTH. HOW FAR WAS SHE FROM THE CAMPSITE? a² + b² = c² 5² + 2² = c² 25 + 4 = c² 29 = c 5. 39 = c ? 5 2 EACH SIDE OF A EQUILATERAL TRIANGLE IS 10 m. FIND THE HEIGHT OF THE TRIANGLE.

PRACTICE EACH SIDE OF A EQUILATERAL TRIANGLE IS 10 m. FIND THE HEIGHT OF THE TRIANGLE. a² + b² = c² a² + 5² = 10² a + 25 = 100 a² = 100 - 25 a= a = 8. 66 10 75 A ROPE IS TIED TO THE TOP OF A 9 ft TENT AND TIED TO A STAKE IN THE GROUND 10 ft FROM THE BASE. HOW LONG IS THE ROPE? a² + b² = c² 9² + 10² = c² 81 + 100 = c² 181 = c² 10 c = 181 c = 13. 45 5 ? 10 9 10 5

FIND THE SQUARE OF EACH: 1. 5² = 5 x 5=25 FIND THE SQUARE ROOT OF EACH: 1. √ 36 = 6 2. 2² = 2 x 2=4 2. √ 168 = 3. 11² = 11 x 11=121 3. √ 625 = 25 4. 8² = 8 x 8=64 4. √ 288 = 5. 12² = 12 x 12=144 5. √ 105 = 6. 15² = 15 x 15=225 6. √ 49 = 7 7. 20² = 20 x 20=400 7. √ 9 = 3 QUIZ ON FRIDAY OVER PYTH. THEOREM!

WARM-UP 5/12/11 TRY THESE ON YOUR OWN, FIND THE HYPOTENUSE FOR EACH: 13 7 8 10 a² + b² = c² 7² + 10² = c² 49 + 100 = c² 149 = c 12. 2 = c 12, 13 a² + b² = c² 8² + 13² = c² 64 + 169 = c² 233 = c 15. 2 = c 15, 16 QUIZ TOMORROW!!!!!!

WARM-UP 5/17/11 A 35 FOOT TELEPHONE POLE NEEDS A SUPPORT WIRE ATTACHED AT THE TOP OF THE POLE TO A POINT IN THE GROUND 20 FEET AWAY FROM THE BASE. ABOUT HOW LONG SHOULD THE WIRE BE? a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² C 40. 31 = c 20 35

A 35 FOOT TELEPHONE POLE NEEDS A SUPPORT WIRE ATTACHED AT THE TOP OF THE POLE, TO A POINT IN THE GROUND 20 FEET AWAY FROM THE BASE. ABOUT HOW LONG SHOULD THE WIRE BE? 35 C 20 a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² 40. 31 = c

A 20 ft FLAGPOLE IS SECURED BY A 25 ft WIRE TO A STAKE IN THE GROUND? HOW FAR FROM THE BASE IS THE STAKE? a² + b² = c² a² + 20² = 25² a² + 400 = 625 a² = 625 - 400 a = √ 225 c 25 a 20 b a = 15 IF A STAIRCASE IS TO FIT INTO A SPACE THAT IS 12 ft HIGH AND 10 ft LONG, HOW LONG IS THE RISER ? 12 10 a² + b² = c² 10² + 12² = c² 100 + 144 = c² 244 = c² √ 244 = c² 15. 62 = c

EXTRA PRACTICE A MAST ON A SAILBOAT IS 10 m TALL. A ROPE IS STRETCHED 15 m FROM THE TOP OF THE MAST TO A CLEAT ON THE DECK. HOW FAR IS THE CLEAT FROM THE BASE OF THE MAST? a² + b² = c² b = 125 10² + b² = 15² b = 11. 2 100 + b² = 225² b² = 225 - 100 b² = 125 15 10 ? TWO JETS LEAVE AN AIRPORT AT THE SAME TIME. ONE WEST AT 400 mph AND THE OTHER NORTHWEST AT 500 mph. HOW FAR APART WERE THE JETS AT THE END OF THE HOUR? 500 ? b = 300 400 a² + b² = c² 400² + b² = 500² 160, 000 + b² = 250, 000² b² = 250000 - 160000 b² = 90, 000

TELL IF IT IS A RIGHT TRIANGLE OR NOT!? !? a² + b² = c² ? 4² + 6² = 7² ? 16 + 36 = 49 52 = 49 7 4 6

PRACTICE TELL IF IT IS A RIGHT TRIANGLE OR NOT! 1. a² + b² = c² 8² + 15² = 17² 17 8 64 + 225 = 289 15 3. 8 9 15 4. 15 20 25 a² + b² = c² 8² + 9² = 15² 64 + 81 = 225 145 = 225 a² + b² = c² 15² + 20² = 25² 225 + 400 = 625 2. 30 10 20 a² + b² = c² 10² + 20² = 30² 100 + 400 = 900 500 = 900 TEST FRIDAY ON PYTHAGOREAN THEOREM AND WARMUPS

Pythagorean Theorem PROBLEM A 35 FOOT TELEPHONE POLE NEEDS A SUPPORT WIRE ATTACHED AT THE TOP OF THE POLE TO A POINT IN THE GROUND 20 FEET AWAY FROM THE BASE. ABOUT HOW LONG SHOULD THE WIRE BE? PROCESS ( SHOW WORK) SOLUTION

WARMUP 5/19/11 A HIGHWAY BRIDGE IS ANCHORED TO THE GROUND BY A RIGHT TRIANGLE. HOW LONG IS THE EMBANKMENT LABELED x 14 a² + b² = c² √ 596 = c² 14² + 20² = c² 196 + 400 = c² 596 = c² 24. 41 = c 24, 25 X 20 TEST TOMORROW!!!! FIND THE MISSING SIDE OF EACH RIGHT TRIANGLE EQUILATERAL SIDES OF 16 a = 16 b = 20 a² + b² = c² 16² + 20² = c² 256 + 400 = c² 656 = c² √ 656 = c 25, 26 25. 61 = c a² + b² = c² 16 a² + 8² = 16² a² + 64 = 256 8 8 a²= 256 - 64 FIND THE HEIGHT a²= 192 a² = √ 192 a = 13. 86 = height 13, 14

AGENDA 5/20/11 1) COMPLETE UNIT TEST **Show all of your work!!! **Check your answers!!! When you are finished with your test and if you are all caught up with your class work, you may go to the computer lab to work in Study Island.

WARMUPS GIVE THE SQUARE ABOVE AND BELOW EACH OF THE GIVEN SQUARE ROOTS. EXAMPLE IS GIVEN USE THE LIST YOU COPIED YESTERDAY

SOLVE EACH

NEW PYTHAG, SQUARES, AREA, ETC

WARMUP If a ladder 39 ft tall is leaned against a building and the base of the ladder is 15 ft from the building, how tall is the building? c a b a² + b² = c² a² + 15² = 39² a² + 225 = 1521 a² = 1521 -225 a² = 1296 a = 36 39 a 15 Item Cost %Disc $Disc S. P. %Tax $Tax F. C. shoe $300 20% $60 $240 10% $24 $264 You should take notes on these for the review for the test on Friday.

Fraction WARMUP Decimal 5. 2425 Percent 500% 24¼% 24. 25% Some of these will be on the Warmup quiz next week. I will give out all answers to review on Thursday.

WARMUP SOLVE EACH: 30² = 900 12² = 144 1² = 1 5² = 18² = 324 13² = 169 17² = 289 7² = 8² = 64 14² = 196 19² = 361 10² = 100 25 49 COMBINE LIKE TERMS: 3 x + 10 – x + 5 - 3 2 x + 12 14 +10 c + 4 c + 12 c + 8 c - 14 34 c We are starting area and perimeter today 12 + 5 – 10 + 2 x 2 x + 7 -22 a + 79 5 – 11 a + 39 Test Friday

WARMUPS GIVE THE SQUARE ABOVE AND BELOW EACH OF THE GIVEN SQUARE ROOTS. EXAMPLE IS GIVEN USE THE LIST YOU COPIED

A and P The area of a rectangle A = l • w is 45 in². One side of it 45 = 5 • 9 is 5 in. What is the perimeter? = 9 + 5 + 9 + 5 = 28 in. WEDNESDAY 9 5 45 in² 5 9 20 The perimeter of rectangle is 60 in. One side is 10 in. What is A=l • w 10 200 in² 10 the area? A = 10 • 20 20 60 -20=40 A = 200 in² The length of a rectangle is 9 cm. The width is 7 cm. What is the area? Perimeter? 9 A=l • w A=9 • 7 A = 63 in² Perimeter = 9+7+9+7 = 32 in. 7 7 9 QUIZ TOMORROW OVER THIS AND THE WKSHTS!!!!!

WEDNESDAY AREA AND PERIMETER CIRCUMFERENCE FIND THE AREA AND PERIMETER OF EACH: CIRCUMFERENCE 8 m 8 m DIAMETER DISTANCE ACROSS THE MIDDLE RADIUS HALF OF THE DIAMETER 3. 14 = =R =D A A = = r² • 3. 14 • 8² 3. 14 • 64 200. 96 C= d • C = 3. 14 • 16 C = 50. 24 IT REALLY HELPS TO WRITE THE FORMULA AND WRITE NEATLY AND PLUG IN THE #’S

WEDNESDAY 5 FIND THE “A or C” A= r² A = 3. 14 • 5² A = 3. 14 • 25 8 C= d C = 3. 14 • 8 A = 25. 12 cm 3 • 8 = 24 A = 78. 5 cm 3 • 25 = 75 Estimate your answer by mult. “ 3 • the whole #”!! A= r² C= d A = 3. 14 • 6² 12 9 C = 3. 14 • 18 A = 3. 14 • 36 A = 56. 25 cm A = 113. 04 cm 3 • 18 = 54 3 • 36 = 108 R=9 D=18 D=12 R=6 IT IS ALWAYS GOOD TO WRITE OUT FORMULA AND THE “D and R” AND THEN ESTIMATE YOUR ANSWER. QUIZ TOMORROW OVER THIS AND THE WKSHTS!!!!!

WARMUP Put the following in order from least to greatest. THURSDAY Which problem situation can be solved with t = 60 w? a. What is t, the # of ounces in w gallons? b. What is t, the volume of a cylinder with a radius of 60 and height of w? c. What is t, the # of hours in w minutes? d. What is t, the # of seconds in w minutes? QUIZ TODAY ON A and P

WARMUP What is the compliment of 15º? THURSDAY 15º 75º What is the suppliment of 35º? 145º 35º Timmy wants to buy a bike for $47. 95 with a 20% discount. About how much will he pay? DISC = $50 • . 20 = $10 $50 – 10 = $40 Which company has the best price? COMPANY HERSHEY MARS SPIRIT CO. NESTLES PRICE 50 - $22. 50 140 - $56 12 - $4. 20. 50 each . 45 22. 50 ÷ 50. 40 56 ÷ 140. 35 4. 20 ÷ 12. 50 QUIZ TODAY ON A and P

WARMUP Solve for Circumference THURSDAY Solve for Area A= r² A = 3. 14 • 7. 5² 15 A = 3. 14 • 56. 25 A = 176. 625 cm² D=15 R=7. 5 3 • 56 = 168 Solve for Area A=l • w A = 8 • 10 8 A = 80 in² 10 P = 36 7 C= d C = 3. 14 • 14 A = 43. 96 cm R=7 D=14 3 • 14 = 42 Solve for Perimeter 21 A=l • w 8 A = 7 • 21 7 A = 147 m² 7 P = 56 21 10 36 – 16 = 20 We will check review and take quick questions, then check hmwk, then take quiz over this material. QUIZ TODAY ON A and P

BE SEATED QUICKLY, HAVE REVIEW READY TO TURN IN, AND GET STARTED ON TEST. YOU NEED TO FINISH BEFORE THE BELL RINGS, IF YOU STUDIED YOU SHOULD DO FINE. WRITE NEATLY ON ANSWER KEY. STARING AT THE TEST WILL NOT GET IT DONE! NO TALKING, NO LOOKING AROUND, SIT UP STRAIGHT, KEEP TEST IN FRONT OF YOU, KEEP YOUR EYES ON YOUR PAPER, DURING TEST Scratch off the 2 nd #57,

TUESDAY Which model represents Which rule can be used to determine the following? m c 2 3 4 5 2 c + 1 4 m - 3 5 9 13 17 4 c - 3 2 m + 1 WARMUP Simplify the following: 6² ÷ 3 • 6 – 2 + 20 36 ÷ 3 • 6 – 2 + 20 12 • 6 – 2 + 20 72 – 2 + 20 70 + 20 90 We will finish the test the last 30 minutes of class.

TUESDAY WARMUP Solve for Circumference Solve for Area A= r² A = 3. 14 • 5² 10 A = 3. 14 • 25 A = 78. 50 cm² D=10 R=5 3 • 25 = 75 FRACTION DECIMAL . 60. 245% 5 C= d C = 3. 14 • 10 A = 31. 40 cm R=5 D=10 3 • 10 = 30 PERCENT 60% 24½% 24. 5% NOTES ON IRREGULAR SHAPES, THEN PRACTICE PROBLEMS, THEN SOME WILL FINISH THE TEST FROM FRIDAY AND THE REST WILL WORK ON WKSHT…. WARMUP QUIZ TOMORROW!!!!!!

TUESDAY AREA AND PERIMETER ANSWER EACH: WHAT IS THE AREA? A=L • W A = 10 • 2 A = 20 cm A=L • W A = 5 • 10 A = 50 cm A=L • W A=1 • 3 A = 3 cm 20 + 50 + 3 = 73 cm² 2 4 5 5 10 10 2 3 1 3 2 2 WHAT IS THE PERIMETER? P = 5 + 4 + 2 + 10 + 2 + 3 + 1 + 2 + 10 = 41 TAKE GOOD NOTES B/C THIS IS WHAT WE ARE DOING TODAY AND TOMORROW

AREA AND PERIMETER FIND “A and P” P = 20 + 12 + 6 + 8 + 6 20 m P = 64 m 25 m A=L • W 6 A = 20 • 12 8 12 A = 240 m² 6 - 48 15 7 A = 192 m² 12 8 7 TUESDAY 5 P = 25 + 8 + 7 + 5 + 13 + 30 = P = 110 m A A = = L • W 30 • 13 = 390 5 • 15 = 75 8 • 7 = 56 A = 521 m² 15 TAKE GOOD NOTES B/C THIS IS WHAT WE ARE DOING TODAY AND TOMORROW 13 ? 30

FIND THE SHADED AREA A and P A=L • W 30 A=L • W A = 30 • 10 5 A = 10 • 10 10 20 A=300 m² 10 5 A = 100 m² 5 5 20 A= r² 10 A=L • W A = 3. 14 • 5² A=300 m² A = 100 m² A = 5 • 20 - A=100 m² + A = 78. 5 m² A = 3. 14 • 25 A =100 m² A = 78. 5 m² A=200 m² A = 178. 5 m² A=L • W 30 m A = 36 • 30 A =1080 m² A=1080 m² 12 12 - A=240 m² 36 m 20 m A=840 m² A=L • W 20 m A = 12 • 20 A=240 m²

WARMUP Look at the 2 rectangles, how would you solve to find if similar? THURSDAY 1. 5 m 3 m 4 m a. b. c. d. Divide 3 by 2 and 4 1. 5 by 4 and 4 by 1. 5 and 3 by 1. 5 and 2 m by 1. 5 2 by 3 4 by 2 to to see see if if quotients are are the the same Mary bought a dozen daises for $3. 75. About how much did she pay for each rose? If there are 3 middle schools, 20 to 30 homerooms, and 25 to 30 students in a class, about how many students are there? NO AFTER SCHOOL TUTORIALS TODAY!

WARMUP A cook estimates that for one month, 240 students will drink milk each day. Each carton cost. 20, what else does he need to know to complete the order. WEDNESDAY a. b. c. d. The The # # of of school days in a month students who do not drink milk students in each class cartons in a case of milk John bought 30 party games priced at 3 for $1. 95 and 56 party favors at 7 for $2. 50. What was the total cost for these items? Steve works at a bank and 30 = 3 • 10 56 = 7 • 8 makes $14. 50 per hour. If he works 35 hrs a week, how 3 @ 1. 95 • 10 19. 50 much does he make in a year? 7 @ 2. 50 • 8 +20. 00 14. 50 • 35 = $507. 50 $39. 50 • 52 weeks $26, 390 NO AFTER SCHOOL TUTORIALS TODAY

THURSDAY WARMUP FIND THE “A and P” OF EACH 12 cm A=L • W 23 cm A = 23 • 5 A = 115 cm 5 1 P = 23 + 5 + 23 + 5 = 56 12 cm 3 1 2 4 11 4 3 cm A A A 9 A = = 7 CHECK HMWK AND THEN WARMUP QUIZ L 7 2 3 • • 2 4 5 20+2 W 4 = 28 11 = 22 12 = 36 A = 86 cm 1 2 4 9 4 7 A=L • W A = 12 • 9 A = 108 cm² - 22 A = 86 cm² P = 12 + 9 + 7 + 4 + 2 + 1 + 3 = 42 cm

THURSDAY 5 FIND THE “A or C” A= r² A = 3. 14 • 5² A = 3. 14 • 25 8 C= d C = 3. 14 • 8 A = 25. 12 cm 3 • 8 = 24 A = 78. 5 cm 3 • 25 = 75 Estimate your answer by mult. “ 3 • the whole #”!! 78. 5 = d A dartboard has a circumference of 78. 5 in. What is the diameter? 78. 5 = 3. 14 • d 25 in A pizza has an area of a 50. 24 in. What is the radius? 50. 24 = r² 50. 24 = 3. 14 • r² 4= r 25 = d 16= r² WARMUP QUIZ TODAY, THEN WKSHT FOR HMWK

JUST WRITE THE FORMULAS AND PLUG IN THE #’S AND SOLVE OTHER FORMULAS A = ½ h(b 1+b 2) HEIGHT A = ½ bh BASE TRIANGLE A = bh 2 A = B • H base 1 HEIGHT TRAPEZOID HEIGHT BASE A = h(b 1+b 2) 2 base 2 PARALLELOGRAM Find the “box” and you have found the height. Find the height and you will find the bases. The bases are always the parallel lines.

AREA AND PERIMETER ANSWER EACH: P=S+S+S+S P=7+6+7 P=5+4+5+4 P = 20 cm WEDNESDAY P = 18 cm A A = = L • W 10 cm² 4 cm² 1 cm² A = 15 cm² A=L • W A=2 • 2=4 x 3 A = 12 cm² A=L • W A=4 • 5 P=S+S+S+S A = 20 cm² P = 5 + 4 + 7 + 2 = P = 18 cm QUIZ TOMORROW OVER THIS AND THE WKSHTS!!!!!

FIND THE AREA 22 6 30 A A A OTHER FORMULAS = = = ½ h(b 1+b 2) ½ 6(22+30) ½ 6(52) 11 ½ (312) 156 m² A = ½ bh A = ½ 10 • 11 A = ½ 110 A = 55 m² 10 PURPLE AREA? 10 30 A A A = = = L • W 30 • 10 300 cm² 150 m² A A = = ½ bh ½ 10 • 30 ½ 300 150 m² THIS WILL BE YOUR HMWK AFTER THE QUIZ, WKSHT 153 AND D 54 ( THE BACK OF TUESDAY HMWK )

WARMUP If Pam buys 5 packages of cheddar cheese, 2 packages of Cajun roast beef, how many lbs will she have? FRIDAY Meat/Cheese Weight/lbs. Per package Brown sugar ham Cajun roast beef Smoked turkey Swiss cheese Cheddar cheese QUIZ OVER NOTES AND WKSHT ON MONDAY, WARMUP QUIZ ON TUESDAY

WARMUP John and three of his friends went to his house after school. His mom had left one half of a cake. Which model shows the correct division of the cake? FRIDAY a. Step 1 Step 2 b. Step 1 Step 2 c. Step 1 Step 2 d. Step 1 Step 2 QUIZ OVER NOTES AND WKSHT ON MONDAY, WARMUP QUIZ ON TUESDAY

FRIDAY FIND “A and C” 9 WARMUP A= r² A = 3. 14 • 4. 5² A = 3. 14 • 20. 25 3 • 20 = 60 A = 63. 585 cm² D=9 R=4. 5 C= d C = 3. 14 • 9 3 • 9 = 27 C = 28. 26 cm YOU WILL SEE SOME LIKE THIS ON THE QUIZ AND TEST FIND THE PURPLE AREA D=20 3 R=10 A= r² A = 3. 14 • 100 3 • 100 = 300 A = 314 cm² 14 3 D=14 R=7 A= r² A = 3. 14 • 7² A = 3. 14 • 49 3 • 49 = 147 A = 153. 86 cm A = 314 - 153. 86 = 160. 14 cm

A and P FIND THE SHADED AREA 22 m A=L • W A = 22 • 10 8 A = 220 m 10 5 A=5 • 8 FRIDAY A = 40 cm A= r² D=22 A = 3. 14 • 121 R=11 r²=121 A = 379. 94 RED AREA? 6 10 m 6 A = 220 – 40 = 180 cm² A=L • W BLUE AREA? 10 m A = 10 • 10 100. 0 m² D=10 r² A = 100 m² -78. 5 m² R=5 A = r²=25 A = 3. 14 • 25 10 m 21. 5 m² A = 78. 5 10 m D=10 R=5 r²=25 A= r² A=379. 94 – 78. 5 A = 3. 14 • 25 A = 301. 44 cm² A = 78. 5

WARMUP FIND THE SHADED AREA A= r² A=L • W A = 3. 14 • 20² 20 20 A = 16 • 16 A = 3. 14 • 400 40 16 A = 1256 m² A = 256 m² D=16 R=8 r²=64 A = 1256 m² ÷ 2 A= r² A = 628 m² A = 3. 14 • 8² A = 3. 14 • 64 16 A = 200. 96 m² 15 30 15 A = L • W A = 30 • 30 A = 100. 48 m² A= r² A=900 +256 m² A = 3. 14 • 15² -353. 25 A = 356. 48 m² A = 3. 14 • 225 546. 75 m² A = 706. 5 m² QUIZ OVER NOTES A = 706. 5 m² ÷ 2 30 AND WKSHT ON MONDAY, WARMUP A = 353. 25 m² FRIDAY QUIZ ON TUESDAY

WARMUP FIND THE PERIMETER AND AREA OF EACH: A=Lx. W A=1/2 bh =7 x 12 =1/2 12 x 8 10 10 =84 m² =1/2 96 8 15 =48 m² A=84+48=132 m² 7 P=7+12+7+10+10=46 m 12 C=πd A=πr² 3. 14 x 20 3. 14 x 10² 62. 8 m 3. 14 x 100 314 m² WARMUP QUIZ THURSDAY WE ARE DOING WKSHT IN CLASS, DUE AT 10 END OF PEIOD, LETS NOT WASTE TIME

WARMUP QUIZ NEXT WEEK FIND THE AREA OF EACH: 1. WHAT IS THE AREA OF A SQUARE WITH THE SIDE OF. 06? A=s². 06 x. 06=. 0036 2. WHAT IS THE AREA OF THE RED SQUARE? A=Lx. W A=πr² 100 -78. 5=21. 5 10 10 x 10=100 =3. 14 x 5² =3. 14 x 25=78. 5 3. FIND THE AREA OF THE FIGURE. A=πr² 1/2 4 =3. 14 x 4² 8 1/2 A=Lx. W =8 x 8=64 8 =3. 14 x 16=50. 24 64+50. 24=114. 24 4

COME IN AND BE READY TO CHECK HMWK, THEN LESSON QUIZ, AFTER QUIZ PICK UP REVIEW FOR TEST. WE WILL CHECK THE REVIEW TOMORROW AND TEST ON WEDNESDAY.

WARMUP Jill’s living room is getting new carpet. The room is 30 ft by 30 ft. Carpet is $12 per yard. How much will 30 ft it cost to carpet her house? (3 ft=1 yd) A=l • w A = 100 • 12 A = 10 • 10 A = $1200 10 yd 30 ft A = 100 MONDAY Which of the following can not be used to find the perimeter of a square? A. s+s+s B. 2 s+2 s C. 4 s 10 yd D. s • s Warmup, then check hmwk, then lesson quiz, then work on review for test on Wednesday

WARMUP The center ring of a water fountain has an area of 91. 6 meters, what is the 5. 4 approximate diameter? 10. 4 = d A= r² 29. 17 = r² 15 91. 6 = 3. 14 • r² 5. 4 = r MONDAY A=½b • h A triangle has a height A = ½ 15 • 14 of 15 inches and a A = ½ (210) base of 14 inches. 14 A = (105 m²) What is the area? The area of a square is 242 m². A second square is half of the first. What is the length of the sides of the second square? A = l • w 121 = 11 • 11 242 m² ÷ 2 121 m² 121 = l • w Warmup, then check hmwk, then lesson quiz, then work on review for test on Wednesday

NO TALKING DURING QUIZ, KEEP YOUR EYES ON YOUR OWN PAPER, SIT UP STRAIGHT, WHEN YOU GET THRU, TURN IT IN AND PICK UP A REVIEW FOR THE TEST. WE WILL CHECK REVIEW TOMORROW AND TEST ON WEDNESDAY.

Which 2 figures have the same area? 12. 5 4 5 WARMUP TUESDAY 12 5 5 8 20 A=l • w A = r² • A =½h • (b 1+b 2) A = ½b • h A = 5 • 12. 5 A = 3. 14 • 16 A =½ 5 • (12+8) A = ½(5 • 20) A = 62. 5 A = 50. 24 A =½ 5 • (20) A = ½(100) A =½ 100 A = 50 A =50 The perimeter of a rectangle is 38 in. One side is 11. 5 7. 5 in, what is the area? 38 -15=23 A=l • w A = 11. 5 • 7. 5 23÷ 2=11. 5 7. 5 A = 86. 25 11. 5

WARMUP A pizza has a circumference of 50. 24 in². What is the radius? C= d • A = r² • 56. 25 = 3. 14 • d A = 3. 14 • 9² 18 = d 9=r A = 3. 14 • 81 A = 254. 34 in² TUESDAY 18 9 A square pizza has an area of 361 in². What are the lengths of the sides? 19 361 = l • w √ 361 = 19 Your pool has a length of 25 m by 12 m, what is the perimeter? 12 P = 12 + 25 + 12 + 25 P = 74 m 25 9 A=361 19

WEDNESDAY FIND THE “diameter” or “radius” of each C= d ? 47. 1 = 3. 14 • d 15 = d 15 ÷ 2 = 7. 5 = r C = 47. 1 m² Solve C= d d= ? √ 63. 69 = r 7. 98 • 2 = d 15. 96 = d d= C= d C = 3. 14 • C C 3. 14 • == r= r² = A= r² C = 3. 14 • 11 C= A= r² 200 m² = 3. 14 • r² 63. 69 = r² 3 5 A= A=

WARMUP WARMUP

FIND THE “diameter” or “radius” of each Find the diameter And you will have some like this on a wksht C= d ? Write formula and plug in 100 = 3. 14 • d #’s to see if you X or ÷ 31. 84 = d ÷ 2 = 15. 92 = r But!!! What if I wanted C = 100 m² the radius? How would I C= d find it? ? 78. 5 = 3. 14 • d ? If the diameter is half 25 = d the radius then I would “ ÷ 2 = 12. 5 = r 2 ÷ ” by 2!! C = 78. 5 m² C = d C = 3. 14 • FRIDAY This works with Area or Circumference TAKE GOOD NOTES B/C THIS IS WHAT WE ARE DOING TODAY AND TOMORROW

HERE IS A SHORTCUT THAT YOU CAN USE SOMETIMES THIS YEAR, IF YOU DON’T GET IT DON’T WORRY, SOME WILL AND THEY CAN USE IT. WHEN EVER YOU ARE SQUARING A # WITH A “ 5” AT THE END, OR A “. 5”……. STEP ONE – SQ. THE 5 STEP TWO – MULTIPLY THE FIRST # BY THE NEXT CONSECUTIVE # 15² = 25, 1 • 2 = 2, so 225 25² = 25, 2 • 3 = 6, so 625 35² = 25, 3 • 4 = 12, so 1225 45² = 2025 55² = 3025

PRACTICE WITH SHORTCUT…. . STEP ONE – SQ. THE 5 STEP TWO – MULTIPLY THE FIRST # BY THE NEXT CONSECUTIVE # 45² = 2025 85² = 7225 95² = 9025 1. 5² =. 25, 1 • 2 = 2, so 2. 25 7. 5² =. 25, 7 • 8 = 6, so 56. 25 5. 5² =. 25, 5 • 6 = 6, so 30. 25 9. 5² =. 25, 9 • 10 = 90, so 90. 25 6. 5² =. 25, 6 • 7 = 90, so 42. 25 115² = 13225 11 • 12 135² = 18225 13 • 14 205² = 42025 20 • 21

SQUARES YOU SHOULD KNOW and REMEMBER 1² = 1 12² = 144 WE HAVE ALREADY 2² = 4 13² = 169 3² = 9 14² = 196 4² = 16 15² = 225 5² = 25 16² = 256 6² = 36 17² = 289 7² = 49 18² = 324 8² = 64 19² = 361 9² = 81 20² = 400 10² = 100 25² = 625 11² = 121 30² = 900 DONE THIS, SO YOU SHOULD KNOW THIS. IF YOU DON’T THEN START LEARNING IT

WARMUP SOLVE EACH EQUATION: x – 25 = 75 x – 25 + 25 = 75 + 25 x = 100 m + 15 - 15 = 100 - 15 m = 85 10 + 25 = c 35 = c THIS IS CALLED THE INVERSE OPERATION, YOU DO THE OPPOSITE TO BOTH SIDES AND SOLVE. PERFECT SQUARES YOU SHOULD KNOW 1² = 1 12² = 144 2² = 4 13² = 169 3² = 9 14² = 196 4² = 16 15² = 225 5² = 25 16² = 256 6² = 36 17² = 289 7² = 49 18² = 324 8² = 64 19² = 361 9² = 81 20² = 400 10² = 100 25² = 625 11² = 121 30² = 900 SOME THINGS WE HAVE DONE AND YOU SHOULD KNOW HOW TO DO AND SOLVE.

FIND THE SQUARE OF EACH: WARMUP FIND THE SQUARE ROOT OF EACH: 1. 5² = 5 x 5=25 1. √ 36 = 6 2. 2² = 2 x 2=4 2. √ 169 = 13 3. 11² = 11 x 11=121 3. √ 625 = 25 4. 8² = 8 x 8=64 4. √ 289 = 17 5. 12² = 12 x 12=144 5. √ 100 = 10 6. 15² = 15 x 15=225 6. √ 49 = 7 7. 20² = 20 x 20=400 7. √ 9 = 3 WE ARE STARTING PYTHAGOREAN THEORUM TODAY. YOU WILL NEED TO KNOW SQ. AND SQ. ROOT!

PRACTICE 25 = n + 8 -8= -8 17 = n 144 = 49 + a - 49 = - 49 95 = a a + 81 = 225 - 81 = - 81 a = 144 a + 36 = 64 - 36 = - 36 a = 28 169 = b + 100 - 100 = - 100 69 = b c = 324 + 324 c = 648