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ICSE-VIII-Mathematics

20: Area of Trapezium and a Polygon Class 8 Maths

with Solutions - page 3

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  • #3-i
    length (ii) area
    Ans : 30 cm(ii) 480 cm2
  • Qstn #4
    The area of a small rectangular plot is 84 m2. If the difference between its length and the breadth is 5 m; find its perimeter.
    Ans : Area of a rectangular plot = 84 m2
    Let breadth = x m
    Then length = (x + 5) m
    Area = l × bx(x + 5) = 84
    ⇒ x 2 + 5x - 84 = 0
    ⇒ x2 + 12x - 7x - 84 = 0
    ⇒ x(x + 12) - 7(x + 12) = 0
    ⇒ (x + 12) (x - 7) = 0
    Either x + 12 = 0, then x = -12 which is not possible being negative
    or, x - 7 = 0, then x = 7
    Length = x + 5 = 7 + 5 = 12m
    and breadth = x = 7 m
    Perimeter = 2(l + b) = 2(12 + 7) = 2 × 19 m = 38 m
  • Qstn #5
    The perimeter of a square is 36 cm; find its area
    Ans : Perimeter of Square = 36 cm
    Side = Perimeter/4
    = 36/4
    = 9 cm
    ∴ Area od Square = Side × Side
    = 9 × 9
    = 81 cm2
  • Qstn #6
    Find the perimeter of a square; whose area is : 1.69 m2
    Ans : Area of square= 1.69 m2
    Side = √area = √1.69 = 1.3 m
    Perimeter = 4 × side = 4 × 1.3 = 5.2 m
  • Qstn #7
    The diagonal of a square is 12 cm long; find its area and length of one side.
    Ans : Let side of square = a cm
    diagonal = 12 cm
    By Pythagoras Theorem, a2 + a2 = (12)2
    2a2 = 144
    ⇒ a2 = 72
    Area of square = a2 = 72 cm2
    a2 = 72
    ⇒ a = √72 = 8.49 cm
  • Qstn #8
    The diagonal of a square is 15 m; find the length of its one side and perimeter.
    Ans : Diagonal of square = 15 m
    Let side of square = a
    a2 + a2 = (15)2 = 225
    ⇒ a2 = 225/2 = 112.50
    ⇒ a = √112.50 = 10.6 m
    Perimeter = 4 × a = 10.6×4 = 42.4 m
  • Qstn #9
    The area of a square is 169 cm2. Find its:
    Ans : Let each side of the square be x cm.
    Its area = x2 = 169 (given)
    x = √169
    ⇒ x = 13 cm
  • #9-i
    one side
    Ans : Thus, side of the square = 13 cm
  • #9-ii
    perimeter
    Ans : Again perimeter = 4 (side) = 4× 13 = 52 cm
  • Qstn #10
    The length of a rectangle is 16 cm and its perimeter is equal to the perimeter of a square with side 12.5 cm. Find the area of the rectangle.
    Ans : Length of the rectangle = 16 cm
    Let its breadth be x cm
    Perimeter = 2 (16 + x) = 32 + 2x
    Also perimeter = 4(12.5) = 50 cm.
    According to statement,
    32 + 2x = 50
    ⇒ 2x = 50 - 32 = 18
    ⇒ x = 9
    Breadth of the rectangle = 9 cm.
    Area of the rectangle (l× b) = 16× 9 = 144 cm2

  • Qstn #11
    The perimeter of a square is numerically equal to its area. Find its area.
    Ans : Let each side of the square be x cm.
    Its perimeter = 4x,
    Area = x2
    By the given condition,4x = x2
    ⇒ x2 - 4x = 0
    ⇒ x (x - 4) = 0
    ⇒ x = 4 [x ≠ 0]
    Area = x2 = (4)2 = 4 x 4 = 16 sq.units.
  • Qstn #12
    Each side of a rectangle is doubled. Find the ratio between :
    Ans : Let length of the rectangle = x
    and breadth of the rectangle = y
  • #12-i
    perimeters of the original rectangle and the resulting rectangle.
    Ans : Perimeter P = 2(x + y)
    Again, new length = 2x
    New breadth = 2y
    ∴ New perimeter P’ = 2(2x + 2y)
    = 4(x + y)
    = 2.2(x + y)
    = 2P
    ∴ P/P’ = ½
    i.e. P : P’
    = 1 : 2
  • #12-ii
    areas of the original rectangle and the resulting rectangle.
    Ans : Area A = xy
    New Area A’ = (2x)(2y) = 4xy
    = 4A
    ∴ A/A’ = ¼
    i.e., A : A’
    = 1 : 4
  • Qstn #13
    In each of the following cases ABCD is a square and PQRS is a rectangle. Find, in each case, the area of the shaded portion.
    (All measurements are in metre).
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