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Mensuration-2D Test 286
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Mensuration-2D Test 286

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  • Question 1/10
    1 / -0.25
    The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?
    Solutions
    Length of two parallel sides of a trapezium = 21 and 9 cm
    Height of trapezium = 10 cm
    Area of trapezium =
  • Question 2/10
    1 / -0.25
    Sides of a triangle are in the ratio 5:12:13 and its area is 480 cm, then what is perimeter of triangle?
    Solutions
    Let length of sides of triangle be 5x, 12x and 13x respectively.
    We 5,12,13 is pythagorean triplet 
    Hence it is a right angled triangle
    So,
    × 5x × 12x = 480
    x2 = 16
    ∴ x = 4
    Perimeter of triangle = 5x + 12x + 13x = 30x
    = 30 × 4 = 120 m
  • Question 3/10
    1 / -0.25
    Three circular discs of radius 7 cm were kept closed together such that the lines joining their centers form a triangle. Find the area of the triangle?
    Solutions
    The triangle is equilateral with side = 14 cm.
    Area of equilateral triangle = √3/4 * a2
    Therefore area = 84.87 cm2
  • Question 4/10
    1 / -0.25
    The length of the diagonal of a rectangle is 26 cm and that of one side is 10 cm. What is the area of this rectangle?
    Solutions
    Angle between adjacent sides of a rectangle = 90 °
    Given that, one side (i.e. length) = 10 cm, and diagonal = 26 cm
    (10,24,26) is a multiple of Pythagoras triplet (5, 12, 13). Thus, breadth will be 24 cm
    Hence, area of the rectangle = l × b
    = 10 × 24
    = 240 sq. cm.
  • Question 5/10
    1 / -0.25
    A sector is formed by opening out a cone of base radius 8 cm and height 6 cm. Then the radius of the sector is (in cm)
    Solutions
    Radius of sector = Slant height of cone

  • Question 6/10
    1 / -0.25
    What is the area (in sq cm) of a circle whose circumference is 22 cm?
    Solutions
    Circumference=22cm
    Let the radius of circle=r
    Then circumference= 2πr = 22

    r=3.5
    area of circle=
  • Question 7/10
    1 / -0.25
    If the perimeter of a rhombus is 40 cm and one of its diagonal is 16 cm, then what is the area (in cm2) of the rhombus?
    Solutions
    Perimeter of a rhombus = 40
    Side of rhombus = 40/4 ⇒ 10 cm each
    One of its diagonal = 16 cm
    Since diagonals of a rhombus bisect each other at 90°.
    1/2×Other diagonal = √(102 - 82)
    ⇒ Other Diagonal = 2×√(100 - 64)
    ⇒ Other Diagonal = 2×√36 
    ⇒ Other diagnol = 12cm

    Area of rhombus = ½ × d1 × d2
    ⇒ ½ × 16 × 12 = 96 
    Hence, the correct option is C
  • Question 8/10
    1 / -0.25
    Find the maximum number of trees which can be planted, 20 metres apart, on the two sides of a straight road 1760 metres long
    Solutions
    Number of trees on each side of the road

    Required answer = 89 × 2 = 178
  • Question 9/10
    1 / -0.25
    ABCD is a trapezium in which AD||BC and AB = DC = 10 m and angle DCB=45o then the distance of AD from BC is
    Solutions

    Put a perpendicular DP on BC.
    angle DPC = 90o
    angle DCP = 45o
    angle PDC = 45o 
    DP = PC
    hence in isosceles right angle triangle DPC
    DP = 10/√2 = 5√2
  • Question 10/10
    1 / -0.25
    The area of rectangle is five times that of a square. The length of the rectangle is 10 cm and the breadth of the rectangle is 5/2 times that of the side of the square, then find the length of the side of square in (in cm) is.
    Solutions
    Side of a square = x cm
    So, area of rectangle = 5 × area of square
    2

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