Length of each side = 4 units To find the area of a square, multiply the length of one side by itself. Area of square = Length x Length = 4 x 4 = 16 square units Therefore, the area of the square is 16 square units.

1. Perimeter & Area
Chapter 10

2. Perimeter
Perimeter - Distance AROUND a plane figure
To measure the PERIMETER of a plane figure, you have to
measure the distance AROUND it.
Explore:
1. Run a piece of yarn around the perimeter of a book.
Mark where you end. Cut the yarn.
2. ESTIMATE the PERIMETER of the book by looking at the
yarn (remember, your pinky is about an inch and your
forearm is about a food)
3. Use a ruler to determine the EXACT PERIMETER of the
book, in inch and centimeter.

3. Perimeter of Polygons
Perimeter - Distance AROUND a plane figure
To measure the PERIMETER of a plane figure, you need to
know the length and width of the polygon
Length - how long the polygon is
Width - how wide the polygon is
Length
Width
To find the perimeter, ADD the measurements of the
sides.

4. Perimeter of a Polygon
Find the PERIMETER of this
book.
1. What shape is the book?
2. How many sides does it
have?
3. What is the Length of the
book?
4. What is the Width of the
book?
5. What MATH do you need to do to find the PERIMETER?

5. Perimeter of a Polygon
Find the PERIMETER of this
book.
1. What shape is the book?
Rectangl
e
2. How many sides does it
have?
3. What is the Length of the
book?
4. What is the Width of the
book?
5. What MATH do you need to do to find the PERIMETER?

6. Perimeter of a Polygon
Find the PERIMETER of this
book.
1. What shape is the book?
Rectangl
e
2. How many sides does it
have? 4 sides
3. What is the Length of the
book?
4. What is the Width of the
book?
5. What MATH do you need to do to find the PERIMETER?

7. Perimeter of a Polygon
Find the PERIMETER of this
book.
1. What shape is the book?
Rectangl
e
2. How many sides does it
have? 4 sides
3. What is the Length of the 32 in
book?
4. What is the Width of the
book?
5. What MATH do you need to do to find the PERIMETER?

8. Perimeter of a Polygon
Find the PERIMETER of this
book.
1. What shape is the book?
Rectangl
e
2. How many sides does it
have? 4 sides
3. What is the Length of the 32 in
book?
20 in
4. What is the Width of the
book?
5. What MATH do you need to do to find the PERIMETER?

9. Add!
20 in + 32 in + 20 in + 32 in = 104 inches (don’t forget
to add all the sides!
Multiply & Add!
(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches

10. Lengt
h
Add!
20 in + 32 in + 20 in + 32 in = 104 inches (don’t forget
to add all the sides!
Multiply & Add!
(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches

11. Lengt
h
Width
Add!
20 in + 32 in + 20 in + 32 in = 104 inches (don’t forget
to add all the sides!
Multiply & Add!
(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches

12. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in

13. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in

14. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in

15. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in

16. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in

17. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in

18. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in
+

19. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in
+

20. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in
+ +

21. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in
+ +

22. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in
+ + +

23. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in
+ + +

24. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in
+ + + +

25. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in
+ + + +

26. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in
+ + + +

27. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in
+ + + +

28. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in
+ + + +

29. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in
+ + + +

30. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in
+ + + +

31. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in
+ + + +

32. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in 9 in
+ + + + +

33. Perimeter
Try these:
Find the PERIMETER of this polygon.
5 in
4 in
6 in 5 in
5 in
6 in
9 in
4 in
3 in
20 in
6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in 9 in
+ + + +
=
+
67in

34. Try Another...

35. Try Another...

37. Answer: 24 feet

38. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
To measure the AREA of a plane figure, you have to count
the number of SQUARE UNITS that will fit inside it without
over lapping.
= 1 square unit
How many could fit
inside this
rectangle?

39. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
To measure the AREA of a plane figure, you have to count
the number of SQUARE UNITS that will fit inside it without
over lapping.
= 1 square unit
How many could fit
inside this
rectangle?

40. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
To measure the AREA of a plane figure, you have to count
the number of SQUARE UNITS that will fit inside it without
over lapping.
= 1 square unit
How many could fit
inside this
rectangle?
24!

41. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
To measure the AREA of a plane figure, you have to count
the number of SQUARE UNITS that will fit inside it without
over lapping.
= 1 square unit
How many could fit
inside this
rectangle?
24!
This rectangle is 24 SQUARE UNITS!

42. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.

43. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.

44. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.
You can place the
figure over the gird
paper.
Count the number
of WHOLE squares.

45. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.
You can place the
figure over the gird
paper. * 1 *
Count the number * 1 1 1 *
of WHOLE squares. 1 1 1 1 1
* 1 1 1 *
* 1 *

46. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.
You can place the
figure over the gird
paper. * 1 *
Count the number * 1 1 1 * About 17
of WHOLE squares. 1 1 1 1 1 Square
* 1 1 1 * Units
* 1 *

47. Area
Area - the number of SQUARE UNITS needed to cover the
figure without overlapping
You can also use a grid paper to estimate the area of a
figure.
You can place the
figure over the gird
paper. * 1 *
Count the number * 1 1 1 * About 17
of WHOLE squares. 1 1 1 1 1 Square
Then add the
partial squares
* 1 1 1 * Units
(*)together to * 1 *
estimate!

48. Area for a Square
To find the area of a Square, you just have to multiply
the length of the side by itself
4 in
4 in x 4 in = 14 square
inch
4 in
We have to say “square”
inch because we ALWAYS
measure AREA in SQUARE
units!

49. Area of a Square
Try this. This square has sides that are 6 feet. Find
the AREA.
6 ft x 6 ft = 36 square
feet
Don’t forget the SQURE
units!

50. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Area of the Rectangle = Length X
Width
Area of this Rectangle =

51. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Length =
4 inches
Area of the Rectangle = Length X
Width
Area of this Rectangle =

52. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Width = 6
inches
Length =
4 inches
Area of the Rectangle = Length X
Width
Area of this Rectangle =

53. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Width = 6
inches
Length =
4 inches
Area of the Rectangle = Length X
Width
4 in x 6 in = 24 square inches
Area of this Rectangle =

54. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Width = 6
inches
Length =
4 inches
Area of the Rectangle = Length X
Width
4 in x 6 in = 24 square inches
Area of this Rectangle =
Don’t forget the SQURE
units!

55. Area of a Rectangle
To find the area of a Rectangle, you just have to
multiply the LENGTH and the WIDTH.
Width = 6
inches
Length =
4 inches
Area of the Rectangle = Length X
Width
4 in x 6 in = 24 square inches
Area of this Rectangle =
Don’t forget the SQURE
units!

56. Try This one...
Find the Area of this Rectangle...

57. Try This one...
Find the Area of this Rectangle...
Length =
7 meters

58. Try This one...
Find the Area of this Rectangle...
Width = 3
meters
Length =
7 meters

59. Try This one...
Find the Area of this Rectangle...
Width = 3
meters
Length =
7 meters
7 in x 3 in = 21 square meters

60. Try This one...
Find the Area of this Rectangle...
Width = 3
meters
Length =
7 meters
7 in x 3 in = 21 square meters
Don’t forget the SQURE
units!

61. Try This one...
Find the Area of this Rectangle...
Width = 3
meters
Length =
7 meters
7 in x 3 in = 21 square meters
Don’t forget the SQURE
units!

62. Find the Pattern
1.Determine the pattern. What will come next?
2.Draw the next 3 figures until you get to the seventh
figure following the pattern.
3.Determine how you would find the PERIMETER.

63. ?

64. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern?
Challenge: What is the
AREA?

65. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
2 + 2 + 2 + 2 + 3 + 3 = 14 in
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern?
Challenge: What is the
AREA?

66. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
2 + 2 + 2 + 2 + 3 + 3 = 14 in
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern? 2+2+2+2+2+2+3+3=
18 in
Challenge: What is the
AREA?

67. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
2 + 2 + 2 + 2 + 3 + 3 = 14 in
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern? 2+2+2+2+2+2+3+3=
18 in
2+2+2+2+2+2+2+2+3+3
= 22 in
Challenge: What is the
AREA?

68. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
2 + 2 + 2 + 2 + 3 + 3 = 14 in
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern? 2+2+2+2+2+2+3+3=
30 18 in
INCHES
2+2+2+2+2+2+2+2+3+3
= 22 in
Challenge: What is the
AREA?

69. The pattern was made 2in
with rectangles that are
3 inches long and 2 3in
inches wide.
2 + 2 + 2 + 2 + 3 + 3 = 14 in
If the pattern is
continued, what will be
the perimeter of the fifth
figure in the pattern? 2+2+2+2+2+2+3+3=
30 18 in
INCHES
2+2+2+2+2+2+2+2+3+3
= 22 in
Challenge: What is the 36
AREA? INCHES

70. 4th figure
5th figure

71. 4th figure
5th figure

72. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure

73. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure

74. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure

75. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure
2+2+2+2+2+2+2+2+2+2+2+2+3+3=
30 in
Or
(2x12) + (3x2) = 24 + 6 = 30 in

76. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure
2+2+2+2+2+2+2+2+2+2+2+2+3+3=
30 in
Or
(2x12) + (3x2) = 24 + 6 = 30 in
Challenge: What is the
AREA?

77. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure
2+2+2+2+2+2+2+2+2+2+2+2+3+3=
30 in
Or
(2x12) + (3x2) = 24 + 6 = 30 in
Challenge: What is the
AREA?
Length = 12 in, Width = 3 in:

78. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure
2+2+2+2+2+2+2+2+2+2+2+2+3+3=
30 in
Or
(2x12) + (3x2) = 24 + 6 = 30 in
Challenge: What is the
AREA?
Length = 12 in, Width = 3 in: x 3 in = 36 square Inches
12in

79. 4th figure
2+2+2+2+2+2+2+2+2+2+3+
3 = 26 in
5th figure
2+2+2+2+2+2+2+2+2+2+2+2+3+3=
30 in
Or
(2x12) + (3x2) = 24 + 6 = 30 in
Challenge: What is the
AREA?
Length = 12 in, Width = 3 in: x 3 in = 36 square Inches
12in
36 SQUARE
INCHES