1. PYTHAGOREAN
THE
THEOREM

2. 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.

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

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

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

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

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

8. DID YOU GET IT RIGHT? a² + b² = c² 12² + 16² = c² 144 + 256 = c²
BE SURE TO WRITE THE FORMULA EACH TIME, PLUG IN THE NUMBERS AND SOLVE

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

10. a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² 40.3 or 40ft = c
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
= c² 35 C
1625 = c²
40.3 or 40ft = c 20

11. Pythagorean Theorem – Day 2x x

12. Try these on your own! x x

13. ? 60 20 WORD PROBLEMS a² + b² = c² b = 375 5² + b² = 20² b = 19.3
A 20ft LADDER IS LEANED AGAINST A WALL. IF THE BASE IS 5ft FROM THE WALL, HOW HIGH CAN YOU CLIMB?
a² + b² = c²
b = 375
5² + b² = 20² 20
b = 19.3 ?
25 + b² = 400
19,20
b² =
b² = 375 5
AS TOM SWAM ACROSS A 60m RIVER, THE CURRENT MOVED HIM 20m DOWNSTREAM. HOW FAR DID HE SWIM?
HELP! HELP!
a² + b² = c²
60² + 20² = c²
² = c²
4000 = c² 60 20
BRODERICK SWIMMING ACROSS THE RIVER
4000 = c²
63.2 = c²
64,65

14. ? a² + b² = c² 9mi 6² + 9² = c² 36 + 81 = c² 6mi 117 = c² 117 = c²
HOW FAR IS THE HELICOPTER FROM IT’S STARTING POINT?
a² + b² = c²
9mi
6² + 9² = c²
= c²
6mi
117 = c²
117 = c²
10.82 = c²
A 35ft LADDER IS LEANED AGAINST A BLDG. HOW HIGH IS THE WINDOW LEDGE ABOVE THE GROUND?
a² + b² = c²
a² = 1000
b = 31.6
35ft
a² + 15² = 35²
a² = ?
a = 1225
a = 31.62
a² =
15ft
31² = 961 and 32² = 1024

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

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

17. ? ? 6 2 5 11 a² + b² = c² 157 = c² 6² + 11² = c² 157 = c 36 + 121 = c²
A BIG SCREEN T.V. IS 6ft WIDE AND 11ft LONG. HOW LONG IS THE DIAGONAL ACROSS THE SCREEN? 11 ?
a² + b² = c²
157 = c² 6
6² + 11² = c²
157 = c
= c²
12.53 = c
KERSTIN LEFT HER CAMPSITE AND HIKED 5mi EAST AND THEN 2mi NORTH. HOW FAR WAS SHE FROM THE CAMPSITE?
a² + b² = c²
29 = c² ?
5² + 2² = c²
29 = c 2 5
= c²
5.39 = c
EACH SIDE OF A EQUILATERAL TRIANGLE IS 10m. FIND THE HEIGHT OF THE TRIANGLE.

18. ? a² + b² = c² a² + 5² = 10² 10 10 a + 25 = 100 a = 8.66 a² = 100 - 25
PRACTICE
EACH SIDE OF A EQUILATERAL TRIANGLE IS 10m. FIND THE HEIGHT OF THE TRIANGLE.
a² + b² = c²
a² + 5² = 10² 10 10
a + 25 = 100
a = 8.66
a² =
a = 75 5 10 5
A ROPE IS TIED TO THE TOP OF A 9ft TENT AND TIED TO A STAKE IN THE GROUND 10ft FROM THE BASE. HOW LONG IS THE ROPE? ? 9 10
a² + b² = c²
c =
9² + 10² = c²
c =
= c²
181 = c²

21. FIND THE SQUARE OF EACH:
FIND THE SQUARE ROOT OF EACH:
1. 5² =
2. 2² =
3. 11² =
4. 8² =
5. 12² =
6. 15² =
7. 20² =
5x5=25
1. √36 =
2. √168 =
3. √625 =
4. √288 =
5. √105 =
6. √49 =
7. √9 = 6
2x2=4
11x11=121 25
8x8=64
12x12=144
15x15=225 7
20x20=400 3
QUIZ ON FRIDAY OVER PYTH. THEOREM!

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

23. a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² 40.31 = c
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
= c² 35 C
1625 = c²
40.31 = c 20

25. a² + b² = c² 35² + 20² = c² 1225 + 400 = c² 1625 = c² 40.31 = c
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
= c² 35
1625 = c² C
40.31 = c 20

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

27. ? ? 15 10 EXTRA PRACTICE a² + b² = c² b = 125 10² + b² = 15² b = 11.2
A MAST ON A SAILBOAT IS 10m TALL. A ROPE IS STRETCHED 15m 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 15
b = 11.2 10
100 + b² = 225²
b² =
b² = 125 ?
TWO JETS LEAVE AN AIRPORT AT THE SAME TIME. ONE WEST AT 400mph AND THE OTHER NORTHWEST AT 500mph. HOW FAR APART WERE THE JETS AT THE END OF THE HOUR?
a² + b² = c²
400² + b² = 500²
160,000 + b² = 250,000²
500 ?
b² =
b = 300
b² = 90,000
400
b² = 90,000

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

29. YES NO YEP TEST FRIDAY ON PYTHAGOREAN THEOREM AND WARMUPS PRACTICE 20
TELL IF IT IS A RIGHT TRIANGLE OR NOT! 20 1.
a² + b² = c² 2.
a² + b² = c²
YES 30 17
8² + 15² = 17²
10² + 20² = 30² 8
= 289
= 900
289 = 289
500 = 900 15 10 NO
a² + b² = c² 3. 8 9
TEST FRIDAY ON PYTHAGOREAN THEOREM AND WARMUPS
8² + 9² = 15²
= 225
145 = 225 15
a² + b² = c² 4. 15
YEP
15² + 20² = 25² 25
= 625
625 = 625 20

30. Pythagorean Theorem PROBLEM PROCESS ( SHOW WORK) SOLUTION
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?

32. FIND THE MISSING SIDE OF EACH RIGHT TRIANGLE
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
24.41 = c
= c²
24,25 X 20
596 = c²
TEST TOMORROW!!!!
FIND THE MISSING SIDE OF EACH RIGHT TRIANGLE
a = 16 b = 20
EQUILATERAL SIDES OF 16
a² + b² = c²
a² + b² = c² 16
16² + 20² = c²
a² + 8² = 16²
= c²
a² + 64 = 256 8 8
656 = c²
a²=
√656 = c
FIND THE HEIGHT
a²= 192
25,26
25.61 = c
a² = √192
a = = height
13,14

34. AGENDA 5/20/11 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.

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

36. SOLVE EACH

37. NEW PYTHAG, SQUARES, AREA, ETC

38. 39 a c a b 15 Item Cost %Disc $Disc S.P. %Tax $Tax F.C. shoe $300 20%
WARMUP
If a ladder 39ft tall is leaned against a building and the base of the ladder is 15ft from the building, how tall is the building?
a² + b² = c² 39
a² + 15² = 39² a c a
a² = 1521
a² =
a² = 1296 b
a = 36 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.

39. 5 500% .2425 24¼% 24.25% WARMUP Fraction Decimal Percent
Some of these will be on the Warmup quiz next week. I will give out all answers to review on Thursday.

40. 12 + 5 – 10 + 2x 3x + 10 – x + 5 - 3 2x + 7 2x + 12 WARMUP SOLVE EACH:
30² =
900
12² =
144
1² = 1
5² = 25
18² =
324
13² =
169
17² =
289
7² = 49
8² = 64
14² =
196
19² =
361
10² =
100
COMBINE LIKE TERMS:
– x
3x + 10 – x 2x
+ 7 2x
+ 12
14 +10c + 4c + 12c + 8c - 14
-22a
+ 79
34c
5 – 11a + 35 – 11a + 39
We are starting area and perimeter today
Test Friday

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

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

43.  = 3.14 = R = D AREA AND PERIMETER CIRCUMFERENCE
WEDNESDAY
AREA AND PERIMETER
CIRCUMFERENCE
FIND THE AREA AND PERIMETER OF EACH:
CIRCUMFERENCE
DIAMETER
DISTANCE ACROSS THE MIDDLE 8m 8m
RADIUS
HALF OF THE DIAMETER
 = 3.14
A =  • r²
C =  • d
A = 3.14 • 8²
C = 3.14 • 16
= R
A = 3.14 • 64
C = 50.24
A =
= D
IT REALLY HELPS TO WRITE THE FORMULA AND WRITE NEATLY AND PLUG IN THE #’S

44. 5 8 12 9 FIND THE “A or C” A =  r² C =  d A = 3.14 • 5² C = 3.14 • 8
WEDNESDAY
FIND THE “A or C”
A =  r²
C =  d 5
A = 3.14 • 5²
C = 3.14 • 8 8
A = 3.14 • 25
A = 25.12cm
3•8 = 24
A = 78.5cm
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 = 56.25cm
A = 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!!!!!

45. Put the following in order from least to greatest.
THURSDAY
WARMUP
Put the following in order from least to greatest.
Which problem situation can be solved with t = 60w?
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

46. COMPANY PRICE HERSHEY 50 - $22.50 MARS 140 - $56 SPIRIT CO. 12 - $4.20
THURSDAY
WARMUP
15º
What is the compliment of 15º?
75º
145º
35º
What is the suppliment of 35º?
Timmy wants to buy a bike for $47.95 with a 20% discount. About how much will he pay?
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
PRICE
HERSHEY
50 - $22.50
MARS
140 - $56
SPIRIT CO.
12 - $4.20
NESTLES
.50 each
÷ 50
÷ 140
÷ 12
.50
QUIZ TODAY ON A and P

47. 15 7 WARMUP Solve for Area Solve for Circumference A =  r² C =  d
THURSDAY
WARMUP
Solve for Area
Solve for Circumference
A =  r²
C =  d
A = 3.14 • 7.5² 15 7
C = 3.14 • 14
A = 3.14 • 56.25
A = 43.96cm
A = cm²
D=15 R=7.5
3•56 = 168
R=7 D=14
3•14 = 42
Solve for Area 10
Solve for Perimeter 21
A = l • w
A = l • w 8
P = 36 8
A = 7 • 21 7
A = 147m² 7
A = 8 • 10
P = 56
A = 80in² 10 21
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

48. 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 2nd #57,

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

50. 10 5 WARMUP Solve for Area Solve for Circumference A =  r² C =  d
TUESDAY
WARMUP
Solve for Area
Solve for Circumference
A =  r²
C =  d
A = 3.14 • 5² 10 5
C = 3.14 • 10
A = 3.14 • 25
A = 31.40cm
A = 78.50cm²
D=10 R=5
3•25 = 75
R=5 D=10
3•10 = 30
FRACTION DECIMAL PERCENT
.60
60%
.245%
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!!!!!!

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

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

53. A and P FIND THE SHADED AREA A = L • W 30 A = L • W A = 30•10 520
A=300m² 10 10 5
A = 100m² 20 5 5
A =  r² 10
A = L • W
A = 3.14•5²
A=300m²
A = 100m²
A = 5•20
A = 3.14•25
- A=100m²
+ A = 78.5m²
A =100m²
A = 78.5m²
A=200m²
A = 178.5m²
A = L • W
30m
A = 36•30
A =1080m²
A=1080m² 12 12
- A=240m²
36m
20m
A=840m²
A = L • W
20m
A = 12•20
A=240m²

54. Look at the 2 rectangles, how would you solve to find if similar?
THURSDAY
WARMUP
Look at the 2 rectangles, how would you solve to find if similar?
1.5m 3m 4m 2m
a. Divide 3 by 2 and 4 by 1.5 to see if quotients are the same
b. Divide 1.5 by 4 and 2 by 3 to see if quotients are the same
c. Divide 4 by 1.5 and 2 by 3 to see if quotients are the same
d. Divide 3 by 1.5 and 4 by 2 to see if quotients are the same
Mary bought a dozen daises for $ About how much did she pay for each rose?
Mary bought a dozen daises for $ 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?
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!

55. WEDNESDAY
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.
a. The # of school days in a month
b. The # of students who do not drink milk
c. The # of students in each class
d. The # of cartons in a case of milk
John bought 30 party games priced at 3 for $1.95 and 56 party favors at 7 for $ What was the total cost for these items?
John bought 30 party games priced at 3 for $1.95 and 56 party favors at 7 for $ What was the total cost for these items?
Steve works at a bank and makes $14.50 per hour. If he works 35hrs a week, how much does he make in a year?
30 = 3•10
56 = 7•8
1.95
•10
19.50
2.50
• 8
+20.00
14.50 • 35 = $507.50
$39.50
•52 weeks
$26,390
NO AFTER SCHOOL TUTORIALS TODAY

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

57. 5 8 25in FIND THE “A or C” A =  r² C =  d A = 3.14 • 5² C = 3.14 • 8
THURSDAY
FIND THE “A or C”
A =  r²
C =  d 5
A = 3.14 • 5²
C = 3.14 • 8 8
A = 3.14 • 25
A = 25.12cm
3•8 = 24
A = 78.5cm
3•25 = 75
Estimate your answer by mult. “3 • the whole #”!!
78.5 =  d
A dartboard has a circumference of 78.5in. What is the diameter?
25in
78.5 = 3.14•d
A pizza has an area of a 50.24in. What is the radius?
25 = d
50.24 =  r²
4= r
50.24 = 3.14•r²
16= r²
WARMUP QUIZ TODAY, THEN WKSHT FOR HMWK

58. JUST WRITE THE FORMULAS AND PLUG IN THE #’S AND SOLVE
OTHER FORMULAS
A = ½ h(b1+b2)
HEIGHT
A = ½ bh
A = h(b1+b2)
A = bh 2
BASE 2
base 1
HEIGHT
TRIANGLE
TRAPEZOID
HEIGHT
base 2
PARALLELOGRAM
BASE
A = B•H
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.

59. QUIZ TOMORROW OVER THIS AND THE WKSHTS!!!!!
WEDNESDAY
AREA AND PERIMETER
A = L • W
ANSWER EACH:
A = 10cm²
P = S + S + S + S
A = 4cm²
P = S + S + S + S
P =
A = 1cm²
P =
P = 20cm
A = 15cm²
P = 18cm
A = L • W
A = 2 • 2 = 4 x3
A = 12cm²
A = L • W
A = 4 • 5
P = S + S + S + S
A = 20cm²
P = =
P = 18cm
QUIZ TOMORROW OVER THIS AND THE WKSHTS!!!!!

60. FIND THE AREA OTHER FORMULAS A = ½ bh A = ½ h(b1+b2) A = ½ 10 • 1122
A = ½ h(b1+b2)
A = ½ 10 • 11
A = ½ 6(22+30) 6
A = ½ 110
A = ½ 6(52)
A = 55m²
A = ½ (312) 11 30
A = 156m² 10
A = L • W
A = ½ bh
PURPLE AREA?
A = ½ 10 • 30
A = 30 • 10
A = ½ 300 10
A = 300cm²
A = 150m²
A = 150m²
A = 150m² 30
THIS WILL BE YOUR HMWK AFTER THE QUIZ, WKSHT 153 AND D54 ( THE BACK OF TUESDAY HMWK )

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

62. FRIDAY
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?
a. Step Step 2
b. Step Step 2
c. Step Step 2
d. Step Step 2
QUIZ OVER NOTES AND WKSHT ON MONDAY, WARMUP QUIZ ON TUESDAY

63. 3 14 14 3 9 WARMUP FIND THE PURPLE AREA FIND “A and C” A =  r²
FRIDAY
WARMUP
FIND THE PURPLE AREA
FIND “A and C”
A =  r²
A = 3.14 • 4.5²
D=20
R=10 3 14 14 3 9
A = 3.14 • 20.25
3•20 = 60
A = cm²
D=9 R=4.5
A =  r²
D=14 R=7
C =  d
A = 3.14 • 10²
A =  r²
C = 3.14 • 9
A = 3.14 • 100
A = 3.14 • 7²
3•9 = 27
3•100 = 300
A = 3.14 • 49
C = 28.26cm
A = 314cm²
3•49 = 147
A = cm
YOU WILL SEE SOME LIKE THIS ON THE QUIZ AND TEST
A = = cm

64. A and P A =  r² D=22 R=11 r²=121 FIND THE SHADED AREA A = 3.14•121
FRIDAY
A and P
A =  r²
D=22 R=11 r²=121
FIND THE SHADED AREA
A = 3.14•121
22m
A = L • W
A =
A = 22 • 10 8
A = 220m 10
RED AREA? 5
A = 5 • 8 6
10m 6
A = 40cm
A = 220 – 40 = 180cm²
A = L • W
BLUE AREA?
D=10 R=5 r²=25
10m
A = 10 • 10
100.0m²
A =  r²
A = 100m²
-78.5m²
A = 3.14•25
10m
21.5m²
A = 78.5
10m
D=10 R=5 r²=25
A =  r²
A= – 78.5
A = 3.14•25
A = cm²
A = 78.5

65. WARMUP FIND THE SHADED AREA A =  r² A = L • W A = 3.14•20² 20 20
FRIDAY
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 = 1256m²
A = 256m²
A = 1256m² ÷ 2
D=16 R=8 r²=64
A =  r²
A = 628m²
A = 3.14•8²
A = 3.14•64 16
A = m²
A = L • W 15 15 30
A = 30•30
A = m²
A =  r²
A=900
+256m²
A = 3.14•15²
A = m²
A = 3.14•225
546.75m²
A = 706.5m²
QUIZ OVER NOTES AND WKSHT ON MONDAY, WARMUP QUIZ ON TUESDAY
A = 706.5m² ÷ 2 30
A = m²

66. WARMUP FIND THE PERIMETER AND AREA OF EACH: A=LxW A=1/2bh =7x12 =84m²
=1/2 96
=48m² 10 10 8 15
A=84+48=132m² 7
P= =46m
WARMUP QUIZ THURSDAY 12
WE ARE DOING WKSHT IN CLASS, DUE AT END OF PEIOD, LETS NOT WASTE TIME
C=πd
A=πr² 10
3.14x20
62.8m
3.14x10²
3.14x100
314m²

67. WARMUP WARMUP QUIZ NEXT WEEK FIND THE AREA OF EACH:
1.WHAT IS THE AREA OF A SQUARE WITH THE SIDE OF .06?
A=s² .06x.06=.0036
2. WHAT IS THE AREA OF THE RED SQUARE?
A=LxW
10x10=100
A=πr²
=3.14x5²
=3.14x25=78.5
=21.5 10
3. FIND THE AREA OF THE FIGURE.
A=πr²
=3.14x4²
=3.14x16=50.24
1/2
A=LxW
=8x8=64 4 4 8 8
1/2
=114.24

68. 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.

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

70. MONDAY
WARMUP
The center ring of a water fountain has an area of 91.6 meters, what is the approximate diameter?
5.4
5.4
10.4 = d
A =  r²
29.17 = r²
91.6 = 3.14• r² 15
5.4 = r
A = ½ b • h
A triangle has a height of 15 inches and a base of 14 inches. What is the area?
A = ½ 15 • 14
A = ½ (210) 14
A = (105m²)
The area of a square is 242m². 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
242m² ÷2
121m²
121 = l • w
Warmup, then check hmwk, then lesson quiz, then work on review for test on Wednesday

72. 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.

73. Which 2 figures have the same area? WARMUP
TUESDAY 12
12.5 5 4 5 5 8 20
A = l • w
A = • r²
A =½h•(b1+b2)
A = ½b • h
A = 5 • 12.5
A = 3.14•16
A =½5•(12+8)
A = ½(5•20)
A = 62.5
A = 50.24
A =½5•(20)
A = ½(100)
A =½100
A = 50
A =50
The perimeter of a rectangle is 38in. One side is 7.5in, what is the area?
11.5
38-15=23
A = l • w
A = 11.5 • 7.5
23÷2=11.5
7.5
7.5
A = 86.25
11.5

74. TUESDAY
WARMUP
A pizza has a circumference of 50.24in². What is the radius? 18
C = • d
A = • r² 9 9
56.25 = 3.14•d
A = 3.14•9²
18 = d
9 = r
A = 3.14 • 81
A = in²
A square pizza has an area of 361in². What are the lengths of the sides?
A=361 19
361 = l • w
√361 = 19
Your pool has a length of 25m by 12m, what is the perimeter? 19 12
P =
P = 74m 25

75. ? ? FIND THE “diameter” or “radius” of each A =  r² C =  d
WEDNESDAY
FIND THE “diameter” or “radius” of each
A =  r²
C =  d
200m² = 3.14 • r² ?
47.1 = 3.14 • d ?
63.69 = r²
15 = d
√63.69 = r
15 ÷ 2 = 7.5 = r
C = 47.1m²
7.98 = r
7.98 • 2 = d
15.96 = d
Solve
d =
d =
r =
r² =
C =  d
C =  d
A =  r²
C = 3.14 •
C = 3.14 •
A = 11 3
C = 3.14 •
C =
C = 5
A =

76. WARMUP

77. ? ? 2 FIND THE “diameter” or “radius” of each Find the diameter
FRIDAY
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 #’s to see if you X or ÷
100 = 3.14 • d
31.84 = d
÷2 = = r
But!!! What if I wanted the radius? How would I find it??
C = 100m²
C =  d
78.5 = 3.14 • d ?
If the diameter is half the radius then I would “ ÷ ” by 2!!
25 = d
÷ 2 = 12.5 = r 2
C = 78.5m²
C =  d
C = 3.14 •
This works with Area or Circumference
TAKE GOOD NOTES B/C THIS IS WHAT WE ARE DOING TODAY AND TOMORROW

78. 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 =
5² = 25, 1•2 = 2, so 225
25² =
5² = 25, 2•3 = 6, so 625
35² =
5² = 25, 3•4 = 12, so 1225
45² =
2025
55² =
3025

79. 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 =
.5² = .25, 1•2 = 2, so 2.25
7.5² =
.5² = .25, 7•8 = 6, so 56.25
5.5² =
.5² = .25, 5•6 = 6, so 30.25
9.5² =
.5² = .25, 9•10 = 90, so 90.25
6.5² =
.5² = .25, 6•7 = 90, so 42.25
115² =
13225
135² =
18225
205² =
42025
11•12
13•14
20•21

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

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

82. WARMUP FIND THE SQUARE OF EACH: FIND THE SQUARE ROOT OF EACH: 1. 5² =
1. 5² =
2. 2² =
3. 11² =
4. 8² =
5. 12² =
6. 15² =
7. 20² =
5x5=25
1. √36 =
2. √169 =
3. √625 =
4. √289 =
5. √100 =
6. √49 =
7. √9 = 6
2x2=4 13
11x11=121 25
8x8=64 17
12x12=144 10
15x15=225 7
20x20=400 3
WE ARE STARTING PYTHAGOREAN THEORUM TODAY. YOU WILL NEED TO KNOW SQ. AND SQ. ROOT!

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

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