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7 th grade Algebra - 13 Perimeter of Plane Shapes

7 th grade Algebra - 13 Perimeter of Plane Shapes. The chapters:. Rectangle’ perimeter Square’s perimeter Triangle’s perimeter Circle’s perimeter Challenge exercises. A. D. What is the perimeter of the following shape?. 8 cm. B. C. 20 cm. Question 1:. 8 cm 160 cm 20 cm

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7 th grade Algebra - 13 Perimeter of Plane Shapes

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  1. 7th grade Algebra - 13 Perimeter of Plane Shapes

  2. The chapters: • Rectangle’ perimeter • Square’s perimeter • Triangle’s perimeter • Circle’s perimeter • Challenge exercises

  3. A D What is the perimeter of the following shape? 8 cm B C 20 cm Question 1: • 8cm • 160cm • 20cm • 56cm

  4. A D What is the perimeter of the following shape? 8 cm B C 20 cm Solution: • 8cm • 160cm • 20cm • 56cm

  5. A D 8 cm B C 20 cm In the following rectangle, the brown line represents the shape’s perimeter. The perimeter of a shape is the distance around the shape. We indicate this distance with the letter P (Perimeter). Let us calculate: The rectangle’s perimeter is 56 cm. P = 2a + 2b = 2(a + b) is the mathematic expression representing the rectangle’s perimeter.

  6. A D b Write a mathematic expression which will represent the rectangle’s perimeter: B C a Question 2: The length of the rectangle is bigger than its width by 5 cm. • P = 2b+5 • P = 2(2b+5) • P = 2a+2b+10 • P = a+b+10

  7. A D b Write a mathematic expression which will represent the rectangle’s perimeter: B C a Solution: The length of the rectangle is bigger than its width by 5 cm. • P = 2b+5 • P = 2(2b+5) • P = 2a+2b+10 • P = a+b+10

  8. A D What is the perimeter of the following shape? a = 8 cm C B a = 8 cm Question 3: • 8cm • 16cm • 32cm • 64cm

  9. A D What is the perimeter of the following shape? a = 8 cm C B a = 8 cm Solution: • 8cm • 16cm • 32cm • 64cm

  10. A D a = 8 cm C B a = 8 cm The perimeter of a this square is the distance around it and it is equal to the sum of the square’s sides. A square is a rectangle with equal sides. Let us calculate: The square’s perimeter is 32 cm. P = 4a is the mathematic expression representing the square’s perimeter.

  11. A D Write a mathematic expression which will represent the square’s side if it’s perimeter P is known: a C B a Question 4:

  12. A D Write a mathematic expression which will represent the square’s side if it’s perimeter P is known: a C B a Solution:

  13. A What is the perimeter of the following shape? c = 5 cm a = 3 cm B C b = 4 cm Question 5: • 8cm • 12cm • 20cm • 17cm

  14. A What is the perimeter of the following shape? c = 5 cm a = 3 cm B C b = 4 cm Solution: • 8cm • 12cm • 20cm • 17cm

  15. A c = 5 cm a = 3 cm B C b = 4 cm The perimeter of a this triangle is the distance around it and it is equal to the sum of the triangle’s sides. Let us calculate: The triangle’s perimeter is 12 cm. The triangle is this example is a right triangle. In this triangle, the hypotenuse is bigger than each of the catheti (legs) and is smaller than their sum. b < c < a + b

  16. Write a mathematic expression which will represent the triangle’s perimeter according to a: A c a B C b Question 6: b is bigger than a by 1, and c is bigger than b by 1. • P = 2a+3 • P = 9a • P = 3a+2 • P = 3a+3

  17. Write a mathematic expression which will represent the triangle’s perimeter according to a: A c a B C b Solution: b is bigger than a by 1, and c is bigger than b by 1. • P = 2a+3 • P = 9a • P = 3a+2 • P = 3a+3

  18. Circle’s perimeter Definition: If the radius of a circle is r, its perimeter will be 2r. If the diameterof a circle is d, its perimeter will be d.  = 3.14

  19. 10 cm What is the circle’s perimeter? Question 6: Perimeter formula: P = 2r = d  = 3.14 • 62.8cm • 31.4cm • 15.74cm • 10cm

  20. 10 cm What is the circle’s perimeter? Solution: Perimeter formula: P = 2r = d  = 3.14 • 62.8cm • 31.4cm • 15.74cm • 10cm

  21. 10 cm Solution: The perimeter formula is: Given: the circle’s perimeter = 10 cm Thus, r = 5 cm We will place the data in the formula: The circle’s perimeter is 31.4 cm. B is the correct answer.

  22. If we increase the circle’s diameter times 2, the circle’s perimeter is: 10 cm Question 7: Perimeter formula: P = 2r = d  = 3.14 • 62.8cm • 31.4cm • 15.74cm • 10cm

  23. If we increase the circle’s diameter times 2, the circle’s perimeter is: 10 cm Solution : Perimeter formula: P = 2r = d  = 3.14 • 62.8cm • 31.4cm • 15.74cm • 10cm

  24. What is the perimeter of the following shape? Question 8: The length of each of the triangles’ side is 1 cm. • 8cm • 16 cm • 24cm • None of the above

  25. What is the perimeter of the following shape? Solution : The length of each of the triangles’ side is 1 cm. • 8cm • 16 cm • 24cm • None of the above

  26. A D B C Solution: The shape’s perimeter is the blue line. We can see that: Each of the shape’s sides is composed of two triangle’s sides. The length of each triangle side is 1 cm. Thus, The shape’s perimeter is: A is the correct answer.

  27. What is the perimeter of the following shape? Question 9: The length of each of the squares’ side is 2 cm. • 48cm • 16 cm • 32cm • 96 cm

  28. What is the perimeter of the following shape? Solution : The length of each of the squares’ side is 2 cm. • 48cm • 16 cm • 32cm • 96 cm

  29. Solution: The shape’s perimeter is the blue line. We can see that the shape’s perimeter contains 16 square sides. Each of the squares’ side is 2 cm. Thus, the shape’s perimeter is: C is the correct answer.

  30. 8 cm A D Each of the following sentences is correct? 5 cm B C 12 cm Question 10: • The shape’s perimeter is smaller than 25 • The shape’s perimeter is smaller than 30 • The shape’s perimeter is larger than 34 • The shape’s perimeter is larger than 30

  31. 8 cm A D Each of the following sentences is correct? 5 cm B C 12 cm Solution : • The shape’s perimeter is smaller than 25 • The shape’s perimeter is smaller than 30 • The shape’s perimeter is larger than 34 • The shape’s perimeter is larger than 30

  32. 8 cm A D 5 cm B C 12 cm Solution: We will calculate the trapeze known sides: In order to calculate the perimeter, we need to add the length of CD to the result. Thus, answer A (smaller than 25) is not correct.

  33. 4 cm D 8 cm A 5 cm 5 cm B C 12 cm Solution: To estimate the length of CD, we will add the dotted lines. In right-angle triangle, the hypotenuseis the longest side, but its length is smaller then the sum of the other two sides. Which means: Thus, the shape’s perimeter cannot be smaller than 30; therefore, answer B is not correct. The perimeter also cannot be larger than 34 based on the same reason, so answer C is also the wrong answer. D is the correct answer.

  34. True ore false? II I III IV V VI Question 11: The perimeter of shape I is 12 units. • True • False

  35. True ore false? II I III IV V VI Solution: The perimeter of shape I is 12 units. • True • False

  36. True ore false? II I III IV V VI Question 12: The perimeter of shape V is equal to the perimeter of shape I + the perimeter of shape II. • True • False

  37. True ore false? II I III IV V VI Solution: The perimeter of shape V is equal to the perimeter of shape I + the perimeter of shape II. • True • False

  38. True ore false? II I III IV V VI Question 13: The perimeter of shape IV is equal to the perimeter of shape VI. • True • False

  39. True ore false? II I III IV V VI Solution: The perimeter of shape IV is equal to the perimeter of shape VI. • True • False

  40. Which of the following shapes has the longest perimeter? A B C D E Question 14:

  41. Which of the following shapes has the longest perimeter? A B C D E Solution:

  42. Are shapes with the same perimeter always have the same area? A B C D E Question 15: Calculate the area and perimeter of the following shapes. • Yes • No

  43. Are shapes with the same perimeter always have the same area? A B C D E Solution: Calculate the area and perimeter of the following shapes. • Yes • No

  44. a = 8 b = 5 c = 3 d = 3 c d What is the perimeter of the following shape? a b Question 16: • 27cm • 32 cm • 16cm • 19 cm

  45. a = 8 b = 5 c = 3 d = 3 c d What is the perimeter of the following shape? a b Solution: • 27cm • 32 cm • 16cm • 19 cm

  46. What is the external perimeter of the following shape? a = 8 b = 5 d = 5 d b a Question 17: • 20.85cm • 28.85 cm • 26cm • 18 cm

  47. What is the external perimeter of the following shape? a = 8 b = 5 d = 5 d b a Solution: • 20.85cm • 28.85 cm • 26cm • 18 cm

  48. Homework • In a rectangle: a = 8 cm ; P = 26 cm ; b = ? • In a square: P = 48 cm ; a = ? • In a circle: P = 15.7 cm ; r = ? • In a triangle: a = 5 cm ; b = 9 cm ; P = 27 cm ; c = ? • The size of a picture that was framed is • The frame width is 4 cm. • What is the external • perimeter of the frame?

  49. ? = b b a Homework Check Question 1: Given: a = 8 cm ; P = 26 cm. • 18cm • 9 cm • 6cm • 5 cm

  50. ? = b b a Solution: Given: a = 8 cm ; P = 26 cm. • 18cm • 9 cm • 6cm • 5 cm

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