Apply Rectangle Area and Perimeter Formulas - 4th Grade Math

1. Find the missing length $l$ if $P = 44$ and $w = 8$ for a rectangle.

   $l = 14$. Use $P = 2l + 2w$: $44 = 2l + 2(8)$, so $l = 14$.

2. Find the missing side $l$ if $P = 44$ yd and $w = 9$ yd.

   $l = 13$ yd. From $P = 2l + 2w$: $44 = 2l + 2(9)$, so $l = 13$ yd.

3. Find the width when a rectangle has area $A = 42$ and length $l = 7$.

   $6$. Use $w = \frac{A}{l} = \frac{42}{7}$.

4. What is the area of a rectangle with $l = 8$ units and $w = 5$ units?

   $40$ square units. Multiply length times width: $8 \times 5 = 40$.

5. What is the perimeter of a rectangle with $l = 6$ and $w = 6$?

   $24$ units. For a square, $P = 4s = 4(6) = 24$ units.

6. Find the length of a rectangle with perimeter $P = 34$ and width $w = 8$.

   $9$. Use $l = \frac{34 - 2(8)}{2} = \frac{18}{2} = 9$.

7. Which expression gives the perimeter of a rectangle with side lengths $l$ and $w$?

   $2(l + w)$. Factored form of perimeter formula: $2(l + w) = 2l + 2w$.

8. Find the length when a rectangle has area $A = 36$ and width $w = 6$.

   $6$. Use $l = \frac{A}{w} = \frac{36}{6}$.

9. A room is $9$ ft long with floor area $72$ ft$^2$. What is the width?

   $8$ ft. Divide area by length: $72 \div 9 = 8$ ft.

10. Which expression equals the area of a rectangle with $L = 6$ and $W = 11$?

    $6 \times 11$. Area is the product of length and width.

11. What is the area of a rectangle that is $12$ ft long and $3$ ft wide?

    $36$ square feet. Multiply length times width: $12 \times 3 = 36$.

12. Find $W$ if $P = 30$ and $L = 10$ for a rectangle.

    $W = 5$. From $P = 2L + 2W$: $30 = 2(10) + 2W$, so $W = 5$.

13. Find and correct the formula error: $A = 2l + 2w$ is labeled as area for a rectangle.

    Correct: $A = l \times w$. The given formula is for perimeter, not area.

14. Find the length when a rectangle has perimeter $P = 24$ and width $w = 4$.

    $8$. Use $l = \frac{24}{2} - 4 = 12 - 4$.

15. A rectangular garden is $15$ m by $3$ m. What is the perimeter in meters?

    $36$. Garden perimeter is $2(15) + 2(3) = 30 + 6 = 36$ m.

16. What is the missing side length if a rectangle has area $A$ and length $l$?

    $w = \frac{A}{l}$. Divide area by length since $A = l \times w$.

17. A room has area $96$ ft$^2$ and length $12$ ft. What is the width?

    $8$ ft. Rearrange $A = l \times w$: $96 \div 12 = 8$ ft.

18. Find the missing width $w$ if $P = 30$ and $l = 10$ for a rectangle.

    $w = 5$. Use $P = 2l + 2w$: $30 = 2(10) + 2w$, so $w = 5$.

19. A rectangle has $P = 36$ and $w = 7$. What is $l$?

    $l = 11$. From $P = 2l + 2w$: $36 = 2l + 2(7)$, so $l = 11$.

20. A room has $A = 63$ square units and $L = 9$ units. What is the width $W$?

    $W = 7$ units. Divide area by length: $63 \div 9 = 7$.

21. Find the missing side $w$ if $A = 35$ m$^2$ and $l = 5$ m.

    $w = 7$ m. Divide area by length: $35 \div 5 = 7$ m.

22. What is the perimeter of a rectangle with $L = 15$ units and $W = 2$ units?

    $34$ units. Apply $P = 2(15) + 2(2) = 30 + 4$.

23. What is the missing factor form for finding length when $A$ and $w$ are known?

    $l = \frac{A}{w}$. Divide area by width since $A = l \times w$.

24. Find the area of a rectangle with $l = 8$ and $w = 6$.

    $48$. Apply $A = l \times w = 8 \times 6 = 48$.

25. Find and correct the formula error: $P = L \times W$ is labeled as perimeter.

    Correct perimeter formula: $P = 2L + 2W$. The given formula is for area, not perimeter.

26. A room is $12$ ft long and $10$ ft wide. What is the floor area in square feet?

    $120$. Floor area uses $A = 12 \times 10 = 120$ sq ft.

27. Find and correct the formula error: $A = 2L + 2W$ is labeled as area.

    Correct area formula: $A = L \times W$. The given formula is for perimeter, not area.

28. Identify the correct unit for area when side lengths are measured in centimeters.

    $\text{cm}^2$. Area is measured in square units of the side lengths.

29. Identify the correct unit for area: inches, square inches, or inches per side.

    square inches. Area measures surface in square units.

30. Find the width of a rectangle with area $A = 35$ and length $l = 7$.

    $5$. Use $w = \frac{A}{l} = \frac{35}{7} = 5$.

31. Identify the missing factor: If $A = 36$ and $W = 4$, what is $L$?

    $L = 9$. Since $A = L \times W$, divide: $36 \div 4 = 9$.

32. A rectangle has perimeter $50$ cm and length $15$ cm. What is the width?

    $10$ cm. From $P = 2l + 2w$: $50 = 2(15) + 2w$, so $w = 10$.

33. Find $L$ if $P = 50$ and $W = 12$ for a rectangle.

    $L = 13$. From $P = 2L + 2W$: $50 = 2L + 2(12)$, so $L = 13$.

34. Find and correct the error: A student wrote $P = l \times w$ for a rectangle.

    Correct: $P = 2l + 2w$. Student confused area formula with perimeter formula.

35. What is the missing length $l$ if a rectangle has $P = 18$ and $w = 4$?

    $l = 5$. From $P = 2l + 2w$: $18 = 2l + 2(4)$, so $l = 5$.

36. Find the width when a rectangle has perimeter $P = 30$ and length $l = 10$.

    $5$. Use $w = \frac{30}{2} - 10 = 15 - 10$.

37. What is the missing side length if a rectangle has area $A$ and width $w$?

    $l = \frac{A}{w}$. Divide area by width since $A = l \times w$.

38. State the formula for the area of a rectangle with length $l$ and width $w$.

    $A = l \times w$. Area equals length times width for rectangles.

39. A picture frame has $l = 11$ in and $w = 7$ in. What is the perimeter?

    $36$ in. Add all sides: $2(11) + 2(7) = 22 + 14 = 36$ in.

40. What is the area of a rectangle with $L = 12$ units and $W = 3$ units?

    $36$ square units. Apply $A = L \times W = 12 \times 3$.

41. Which expression equals the perimeter of a rectangle with $L = 6$ and $W = 11$?

    $2(6 + 11)$. Perimeter formula factored: $P = 2(L + W)$.

42. Identify the missing factor: If $A = 42$ and $L = 7$, what is $W$?

    $W = 6$. Since $A = L \times W$, divide: $42 \div 7 = 6$.

43. What is the perimeter of a rectangle with $l = 9$ units and $w = 4$ units?

    $26$ units. Add all sides: $2(9) + 2(4) = 18 + 8 = 26$.

44. A rectangle has area $A = 48$. If $L = 6$, what is $W$?

    $W = 8$. Divide area by length: $48 \div 6 = 8$.

45. A rectangle has area $A = 64$. If $l = 16$, what is $w$?

    $4$. Solve $64 = 16 \times w$, so $w = 4$.

46. Find the missing length $l$ if $A = 63$ and $w = 7$ for a rectangle.

    $l = 9$. Divide area by width: $63 \div 7 = 9$.

47. What is the perimeter of a rectangle that is $12$ ft long and $3$ ft wide?

    $30$ feet. Add all sides: $2(12) + 2(3) = 24 + 6 = 30$.

48. What is the total area of $2$ identical rectangles, each with $A = 18$ square units?

    $36$ square units. Add the areas: $18 + 18 = 36$ square units.

49. What is the missing length $l$ if a rectangle has $A = 54$ and $w = 6$?

    $l = 9$. Divide area by width: $54 \div 6 = 9$.

50. State the perimeter formula written as a multiplication expression for a rectangle.

    $P = 2(l + w)$. Factor out 2 from the sum of length and width.

51. State the formula for the perimeter of a rectangle with length $l$ and width $w$.

    $P = 2l + 2w$. Add all four sides: two lengths plus two widths.

52. A rectangle has perimeter $P = 36$. If $W = 7$, what is $L$?

    $L = 11$. Solve $36 = 2L + 2(7)$ to get $L = 11$.

53. What is the perimeter of a rectangle with $l = 9$ and $w = 4$?

    $26$ units. Add all sides: $2(9) + 2(4) = 18 + 8 = 26$.

54. Find and correct the formula error: $P = l \times w$ is labeled as rectangle perimeter.

    Correct: $P = 2l + 2w$. $l \times w$ gives area, not perimeter.

55. Identify the correct unit for perimeter: square feet or feet.

    feet. Perimeter measures distance in linear units.

56. Find the area of a $7$ by $10$ rectangular garden.

    $70$ square units. Multiply length by width: $7 \times 10$.

57. Which expression matches the perimeter of a rectangle: $l + w$ or $2(l + w)$?

    $2(l + w)$. Perimeter adds all sides, which is $2(l + w)$.

58. What is the missing width $w$ if a rectangle has $A = 42$ and $l = 7$?

    $w = 6$. Divide area by length: $42 \div 7 = 6$.

59. Find the perimeter of a rectangle with $l = 9$ and $w = 4$.

    $26$. Apply $P = 2(9) + 2(4) = 18 + 8 = 26$.

60. A rectangle has $P = 28$ units and $L = 8$ units. What is the width $W$?

    $W = 6$ units. Solve $28 = 2(8) + 2W$ to get $W = 6$.

61. Identify the correct unit for the perimeter of a $6$ cm by $2$ cm rectangle.

    centimeters ($\text{cm}$). Perimeter is a linear measurement.

62. Identify the error: A student says the perimeter formula is $P = l \times w$.

    Correct formula: $P = 2l + 2w$. Student confused area formula with perimeter formula.

63. Find and correct the error: A student wrote $A = 2l + 2w$ for a rectangle.

    Correct: $A = l \times w$. Student confused perimeter formula with area formula.

64. Identify the correct unit for perimeter when side lengths are measured in centimeters.

    centimeters, $\text{cm}$. Perimeter uses the same linear unit as the sides.

65. A rectangular rug is $12$ ft by $3$ ft. What is its area?

    $36$ square feet. Apply area formula: $12 \times 3 = 36$ square feet.

66. Identify the correct unit for the area of a $6$ cm by $2$ cm rectangle.

    square centimeters ($\text{cm}^2$). Area is measured in square units.

67. What is the missing width $w$ if a rectangle has $P = 30$ and $l = 10$?

    $w = 5$. From $P = 2l + 2w$: $30 = 2(10) + 2w$, so $w = 5$.

68. What is the area of a rectangle with $l = 8$ and $w = 5$?

    $40$ square units. Multiply length times width: $8 \times 5 = 40$.

69. A garden is $15$ m by $3$ m. What is the perimeter in meters?

    $36\ \text{m}$. Garden perimeter = $2(15) + 2(3)$ meters.

70. Identify the missing number: $A = 6 \times \square$ and $A = 48$.

    $8$. Find the missing factor: $48 \div 6 = 8$.

71. Find the length of a rectangle with area $A = 54$ and width $w = 6$.

    $9$. Use $l = \frac{A}{w} = \frac{54}{6} = 9$.

72. A rectangle has perimeter $P = 24$ and width $w = 5$. What is the length $l$?

    $7$. Solve $24 = 2l + 2(5)$, so $2l = 14$ and $l = 7$.

73. Find the perimeter of a $7$ by $10$ rectangular garden.

    $34$ units. Add all sides: $2(7) + 2(10) = 14 + 20$.

74. What is the area of a rectangle with $l = 11$ and $w = 1$?

    $11$ square units. Multiply length times width: $11 \times 1 = 11$.

75. Find the missing width $w$ if $A = 48$ and $l = 6$ for a rectangle.

    $w = 8$. Divide area by length: $48 \div 6 = 8$.

76. A room is $12$ ft by $9$ ft. What is the area of the floor in $\text{ft}^2$?

    $108\ \text{ft}^2$. Floor area = $12 \times 9$ square feet.

77. Identify the correct unit for perimeter when side lengths are measured in meters.

    $\text{m}$. Perimeter uses the same linear unit as the sides.

78. Find the width of a rectangle with perimeter $P = 30$ and length $l = 9$.

    $6$. Use $w = \frac{30 - 2(9)}{2} = \frac{12}{2} = 6$.

79. A rectangular garden is $7$ m by $2$ m. What is its perimeter?

    $18$ meters. Apply perimeter formula: $2(7) + 2(2) = 18$ meters.

80. Identify the correct unit for area when side lengths are measured in meters.

    square meters, $\text{m}^2$. Area units are squared since we multiply two lengths.

81. State the perimeter formula written using parentheses for a rectangle with length $l$ and width $w$.

    $P = 2(l + w)$. Factor out 2 from the sum of length and width.

82. A rectangle has $A = 72$ and $w = 9$. What is $l$?

    $l = 8$. Divide area by width: $72 \div 9 = 8$.

83. What is the missing factor form for finding width when $A$ and $l$ are known?

    $w = \frac{A}{l}$. Divide area by length since $A = l \times w$.

Study these flashcards