2. WARM UP 11/30/15 Write down one fun thing that you did over Thanksgiving Weekend; turn to a neighbor and share 1

3. 2 PERIMETER

4. 3 Perimeter Perimeter is defined as the distance around an object or shape.

5. 4 Rules to find the perimeter Rule 1:Measure the length of all sides of the shape. Rule 2:Add all the measured sides of the shape. The sum of all the sides gives the perimeter.

6. 5 Example: Find the perimeter of the given rectangle. Perimeter of the given rectangle is = 11 + 5 + 11 + 5 = 32 cm 5 cm 11 cm

7. 6 Perimeter of square Perimeter of the shape when all the sides of the shape are equal = 4 x length of side Example – Perimeter of square 4 cm Perimeter of square = 4 x side = 4 x 4 = 16 cm

8. 7 Perimeter  Perimeter obeys Commutative property of addition.  Perimeter of the rectangle does not change if the lengths of the sides are added in a different order.

9. 8 Find the perimeter of the hexagon given below. Answer- 18 cm 3 cm

10. 9 Important Tips  Two different polygons can have the same perimeter.  Perimeter can be calculated only of the closed figure.

11. 10 13 match sticks are used to make a hut on the paper. If each match stick is 3 cm long, what is the perimeter of the hut?

12. 11 What is the perimeter of the given figure? a) 36 cm b) 22 cm c) 28 cm d) None of these 5 cm 2 cm

13. 12 The perimeter of the figure given below is 152 cm. Find the missing side. 6 cm 40 cm 11 cm

14. 13 If each side of the pentagon is 8 cm, what is the perimeter of the pentagon?

15. copyright@Ed2netLearning,Inc14 The Perimeter of a small room is 140 feet. If the room is rectangular shape and it is 40 feet wide, what is the width?

16. 15 ASSESSMENT

17. 16 1.What is the perimeter of the equilateral triangle with side of 8 cm?

18. 17 2.How much ribbon is required to cover the outer boundary of the figure given below? 6 cm 4 cm 3 cm 3.If each centimeter of the ribbon costs $0.05, how much does it cost for the ribbon? (problem #2)

19. copyright@Ed2netLearning,Inc18 4.If the Perimeter of the square garden is 64 cm. What is the side of the square?

20. copyright@Ed2netLearning,Inc19 5.Lara’s garden is 13 ft long and 9 ft wide. She wants to put a fence around it. How much fencing will Lara need?

21. 20 6.How can you find the perimeter of a rhombus if the length of one side of rhombus is p cm? a) 4 x p cm b) 4 + p cm c) 4 – p cm d) None of these

22. 21 7.Find the perimeter of the figure given below (trapezium). 9 cm 12 cm 5 cm

23. 22 8.John ran twice around a square park; each side of the square has a length of 7 m. How much distance did he cover?

24. 23 9.Find the Perimeter of the given figure. 8 cm 6cm 4 cm 2 cm

25. WARM UP 12/1/15 Solve the following rebus puzzles 24

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29. The area of a shape is a measure of how much surface the shape takes up. Area For example, which of these rugs covers a larger surface? Rug A Rug B Rug C

30. Area of a rectangle Area is measured in square units. We can use mm 2, cm 2, m 2 or km 2. The 2 tells us that there are two dimensions, length and width. We can find the area of a rectangle by multiplying the length and the width of the rectangle together. length, l width, w Area of a rectangle = length × width = lw

31. Area of a rectangle What is the area of this rectangle? 8 cm 4 cm Area of a rectangle = lw = 8 cm × 4 cm = 32 cm 2

32. Area of a right-angled triangle What proportion of this rectangle has been shaded? 8 cm 4 cm What is the shape of the shaded part? What is the area of this right-angled triangle? Area of the triangle = × 8 × 4 = 1 2 4 × 4 = 16 cm 2

33. We can use a formula to find the area of a right-angled triangle: Area of a right-angled triangle base, b height, h Area of a triangle = 1 2 × base × height = 1 2 bh

34. Area of a right-angled triangle Calculate the area of this right-angled triangle. 6 cm 8 cm 10 cm To work out the area of this triangle we only need the length of the base and the height. We can ignore the third length opposite the right angle. Area = 1 2 × base × height = × 8 × 6 1 2 = 24 cm 2

35. Area of shapes made from rectangles How can we find the area of this shape? 7 m 10 m 8 m 5 m 15 m We can think of this shape as being made up of two rectangles. Either like this … … or like this. Label the rectangles A and B. A B Area A = 10 × 7 = 70 m 2 Area B = 5 × 15 = 75 m 2 Total area = 70 + 75 = 145 m 2

36. Area of shapes made from rectangles How can we find the area of the shaded shape? We can think of this shape as being made up of one rectangle with another rectangle cut out of it. 7 cm 8 cm 3 cm 4 cm Label the rectangles A and B. A B Area A = 7 × 8 = 56 cm 2 Area B = 3 × 4 = 12 cm 2 Total area = 56 – 12 = 44 cm 2

37. E D C B A Area of an irregular shapes on a pegboard We can divide the shape into right-angled triangles and a square. Area A = ½ × 2 × 3 = 3 units 2 Area B = ½ × 2 × 4 = 4 units 2 Area C = ½ × 1 × 3 = 1.5 units 2 Area D = ½ × 1 × 2 = 1 unit 2 Area E = 1 unit 2 Total shaded area = 10.5 units 2 How can we find the area of this irregular quadrilateral constructed on a pegboard?

38. C DBA Area of an irregular shapes on a pegboard An alternative method would be to construct a rectangle that passes through each of the vertices. The area of this rectangle is 4 × 5 = 20 units 2 The area of the irregular quadrilateral is found by subtracting the area of each of these triangles. How can we find the area of this irregular quadrilateral constructed on a pegboard?

39. Area of an irregular shapes on a pegboard Area A = ½ × 2 × 3 = 3 units 2 AB CD Area B = ½ × 2 × 4 = 4 units 2 Area C = ½ × 1 × 2 = 1 units 2 Area D = ½ × 1 × 3 = 1.5 units 2 Total shaded area = 9.5 units 2 Area of irregular quadrilateral = (20 – 9.5) units 2 = 10.5 units 2 How can we find the area of this irregular quadrilateral constructed on a pegboard?

40. Area of a triangle What proportion of this rectangle has been shaded? 8 cm 4 cm Drawing a line here might help. What is the area of this triangle? Area of the triangle = × 8 × 4 = 1 2 4 × 4 =16 cm 2

41. Area of a triangle The area of any triangle can be found using the formula: Area of a triangle = × base × perpendicular height 1 2 base perpendicular height Or using letter symbols: Area of a triangle = bh 1 2

42. Area of a triangle What is the area of this triangle? Area of a triangle = bh 1 2 7 cm 6 cm = 1 2 × 7 × 6 = 21 cm 2

43. Area of a parallelogram Area of a parallelogram = base × perpendicular height base perpendicular height The area of any parallelogram can be found using the formula: Or using letter symbols: Area of a parallelogram = bh

44. Area of a parallelogram What is the area of this parallelogram? Area of a parallelogram = bh 12 cm 7 cm = 7 × 12 = 84 cm 2 8 cm We can ignore this length

45. Area of a trapezium The area of any trapezium can be found using the formula: Area of a trapezium = (sum of parallel sides) × height 1 2 Or using letter symbols: Area of a trapezium = ( a + b ) h 1 2 perpendicular height a b

46. Area of a trapezium 9 m 6 m 14 m Area of a trapezium = ( a + b ) h 1 2 = (6 + 14) × 9 1 2 = × 20 × 9 1 2 = 90 m 2 What is the area of this trapezium?

47. Area of a trapezium What is the area of this trapezium? Area of a trapezium = ( a + b ) h 1 2 = (8 + 3) × 12 1 2 = × 11 × 12 1 2 = 66 m 2 8 m 3 m 12 m

48. Area problems 7 cm 10 cm What is the area of the yellow square? We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square. If the height of each blue triangle is 7 cm, then the base is3 cm. Area of each blue triangle = ½ × 7 × 3 = ½ × 21 = 10.5 cm 2 3 cm This diagram shows a yellow square inside a blue square.

49. Area problems 7 cm 10 cm We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square. There are four blue triangles so: Area of four triangles = 4 × 10.5 = 42 cm 2 Area of blue square = 10 × 10 = 100 cm 2 Area of yellow square = 100 – 42 = 58 cm 2 3 cm This diagram shows a yellow square inside a blue square. What is the area of the yellow square?

50. Area formulae of 2-D shapes You should know the following formulae: b h Area of a triangle = bh 1 2 Area of a parallelogram = bh Area of a trapezium = ( a + b ) h 1 2 b h a h b

51. Using units in formulae Remember, when using formulae we must make sure that all values are written in the same units. For example, find the area of this trapezium. 76 cm 1.24 m 518 mm Let’s write all the lengths in cm. 518 mm = 51.8 cm 1.24 m = 124 cm Area of the trapezium = ½(76 + 124) × 51.8 = ½ × 200 × 51.8 = 5180 cm 2 Don’t forget to put the units at the end.

52. WARM UP 12/2/15 Solve the following rebus puzzles

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56. Surface Area

57. Rectangular Prism The surface area S.A. of a rectangular prism with base l, width w, and height h is the sum of the areas of its faces. S.A. = 2lh + 2lw + 2hw

58. Practice Problem 1  Find the surface area of the rectangular prism shown to the right.

59. Triangular Prism To find the surface area of a triangular prism, it is more efficient to find the area of each face and calculate the sum of all of the faces.

60. Practice Problem 2 Find the surface area of the triangular prism shown to the right. Find the area of each shape and add. Area of rectangle 1Area of rectangle 2Area of rectangle 3 Area of the triangles

61. WARM UP 12/3/15 How many faces are in the following pictures? 60

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65. VOLUME

66. What is Volume?  Volume is the measure of the capacity of a container.  It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

67. Cubic Units  Volume is measured in cubic units.  Use cubes to fill a rectangular prism such as a box.

68. One Cubic Unit 1 unit (height) 1 unit (length) 1 unit (width) A unit might be measured in inches, feet, centimeters, etc.

69. How many cubic units is this rectangle? What did you find? Yes, it is 8 cubic units!

70. How about this one? Remember… there are some cubes you can’t see! Watch...

71. Now Count Them What did you find? Yes! There are 12 cubic units!

72. What’s the formula? The formula for finding the volume of a rectangle is …. L x W x H = Volume This means we take the length times the width, then multiply that by the height.

73. Let’s try it! L = 3 H = 3 W = 2 3 x 3 x 2 = 18 cubic units

74. Find the volume of this one! What did you find? 4 x 2 x 3 = 24 cubic units

75. Volume and Surface Area The volume V and surface area S of a cube with side lengths of s are given by the formulas: V = s 3 Volume and Surface Area of a Cube s s s 5 ft. Find the volume and surface area of the cube below. V = 5 3 S = 6  (5) 2 V = 125ft. 3 S = 6  25 S = 150ft. 2 and S = 6  s 2

76. Volume and Surface Area Volume is a measure of capacity of a space figure. It is always measured in cubic units. Surface Area is the total region bound by two dimensions. It is always measured in square units. w h l The volume V and surface area S of a box with length l, width w, and height h is given by the formulas: V = l  w  h Volume and Surface Area of a Rectangular solid (box) and S = 2  l  w + 2  l  h + 2  h  w

77. 9-476 2 in. 3 in. 7 in. Find the volume and surface area of the box below. V = 7(2)(3) V = 42in. 3 S = 2(7)(2) + 2(7)(3) + 2(3)(2) S = 28 + 42 + 12 S = 82in. 2

78. Volume and Surface Area Volume of a Pyramid The volume V of a pyramid with height h and base of area B is given by the formula: Find the volume of the pyramid (rectangular base) below. cm 3 Note: B represents the area of the base (l w). 7 cm 6 cm 3 cm

79. WARM UP 12/4/15 78

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83. Circumference, Area of a Circle

84. Circles AA circle is the set of all points in a plane that are the same distance from a given point, called the center.

85. The diameter (d) is the distance across a circle through the center of the circle. The radius (r) is the distance from the center to any point on the circle. The circumference (C) is the distance around a circle.

86. PPi is a non-terminating and non-repeating number represented by the Greek letter  (pi) 33.14 is often used as an approximation for .

87. Pi is number that is approximately equal to 3.14. It is the number you get if you divide the circumference of any circle by its diameter. It's the same for all circles. You can approximate pi for yourself by taking some circular things like the tops of jars and CD's and frisbees and measuring their diameter and their circumference. When you divide the circumference by the diameter, you'll get an answer something like 3.14. It will be the same every time (unless you measured wrong). Use think link to learn more! https://www.youtube.com/watch?v=DLZMZ- CT7YU

88. Circles FFormulas for finding Circumference CC =  d CC = 2  r IIf you are given the diameter in a problem use the formula with d. If you are given a problem with the radius use the formula with r. BBoth formulas find the circumference.

89. Find Circumference 21 in Which formula for C will you use? C = 2  r C = 2  (21) C = 131.9 inches

90. Your Turn Find the Circumference 4.5cm Which formula for C will you use? C =  d C =  (4.5) C = 14.1cm

91. Circles - Area FFormula for finding the area of a circle: AA =  r IIf you are given the diameter instead of the radius; divide the diameter by 2 to get the radius. 2

92. Find the Area 14m D = 14 m r = ? 14 ÷ 2 = 7 m A =  r A =  (7 ) A =  (49) A = 153.9 m 2 2 2

93. Your Turn Find the Area 5 ft A =  r A =  (5 ) A =  (25) A = 78.5 ft 2 2 2

94. Surface Area of a Cylinder  The surface area S.A. of a cylinder with height h and radius r is the area of the two bases plus the area of the curved surface (parallelogram). ModelNetArea 2 circular bases 2 congruent circles with radius r 1 curved surface 1 rectangle with width h and length

95. Practice Problem  Find the surface area of the cylinder. Round your answers to the nearest hundredth.

96. Volume of Surface Area of a Right Circular Cylinder 10 m 2 m The volume V and surface area S of a right circular cylinder with base radius r and height h are given by the formulas: Volume and Surface Area Find the volume and surface area of the cylinder below. V =  (2) 2 (10) V = 40  V = 125.6m3m3 S = 2  (2)(10) + 2  (2) 2 S = 40  + 8  = 48  S = 150.72 m2m2 V =  r 2 h h r and S = 2  rh + 2  r 2

97. Volume of Surface Area of a Sphere r The volume V and surface area S of a sphere radius r are given by the formulas: Volume and Surface Area V = (4/3)  r 3 Find the volume and surface area of the sphere below. 9 in. S = 4  (9) 2 V = (4/3)  (9) 3 V = 972  V = 3052.08in. 3 S = 324  S = 1017.36 in. 2 and S = 4  r 2

98. Volume and Surface Area Volume of Surface Area of a Right Circular Cone The volume V and surface area S of a right circular cone with base radius r and height h are given by the formulas:

99. Find the volume and surface area of the cone below. V = (1/3)  (3) 2 (4) V = 12  V = 37.68m3m3 S = 15  + 9  S = 24  S = 75.36m2m2 h = 4 m r = 3 m