Area and Perimeter

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Aptitude miscellaneous
  1. In Δ ABC ,sides BC = 10 cm and height AD = 4.4 cm. If AC = 11 cm. Then altitude BE equals ?








  1. View Hint View Answer Discuss in Forum

    We know that area of triangle = ( base x height ) / 2
    So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
    ⇒ (10 x 4.4) / 2 = (11 x h) / 2
    ⇒ h= (10 x 4.4)/11 = 4 cm

    Correct Option: B

    We know that area of triangle = ( base x height ) / 2
    So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
    ⇒ (10 x 4.4) / 2 = (11 x h) / 2
    ⇒ h= (10 x 4.4)/11 = 4 cm

  1. The cross section of a canal is a trapezium in shape . If the canal is a trapezium in shape. If the canal is 10 meters wide at the top and 6 meters wide at bottom and the area of cross section is 640 sq. meters The depth of canal is ?








  1. View Hint View Answer Discuss in Forum

    Cross section area = 1/2 x ( a + b ) x d
    Where a and b are the parallel sides, d is the perpendicular distance between them.

    Correct Option: B

    Cross section area = 1/2 x ( a + b ) x d
    where a and b are the parallel sides, d is the perpendicular distance between them.
    ⇒ 1/2 x ( a + b ) x d = 640
    ⇒ d = (640 x 2) / 16 = 80m

  1. The area of a trapezium is 384 sq.cm. If its parallel sides in ratio 3 : 5 and the perpendicular distance between them be 12 cm. The smaller of parallel sides is ?








  1. View Hint View Answer Discuss in Forum

    Let the parallel sides be 3a and 5a.
    So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.
    ⇒ 1/2 (3a +5a) x 12 = 384

    Correct Option: B

    Let the parallel sides be 3a and 5a.
    So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.
    ⇒ 1/2 (3a +5a) x 12 = 384
    ⇒ 8a = 64
    ∴ a =8

    ∴ Smaller side = 3x = 3 x 8 = 24 cm.

  1. The two parallel sides of a trapezium are 1 meters and 2 meters respectively . The perpendicular distance between them is 6 meters. The area of the trapezium is ?








  1. View Hint View Answer Discuss in Forum

    Area of trapezium = 1/2 x sum of parallel sides x perpendicular distance between them

    Correct Option: C

    Area of trapezium = 1/2 x sum of parallel sides x perpendicular distance between them
    = 1/2 (1 + 2) x 6 m2
    = 9 m2

  1. A parallelogram has sides 60 m and 40 m and one of the diagonal is 80 m long. Then its area is ?








  1. View Hint View Answer Discuss in Forum

    AB = 60 m, BC = 40 m and AC = 80 m
    ∴ s = (60 + 40 + 80 ) / 2 m = 90 m
    (s-a) = 90 - 60 = 30 m,
    (s-b) = 90 - 40 = 50 m and
    (s-c) = 90 - 80 = 10 m

    ∴ Area of Δ ABC =
    √s(s-a)(s-b)(s-c)
    = √90 x 30 x 50 x 10 m2
    = 300√15 m2

    Correct Option: C

    AB = 60 m, BC = 40 m and AC = 80 m
    ∴ s = (60 + 40 + 80 ) / 2 m = 90 m
    (s-a) = 90 - 60 = 30 m,
    (s-b) = 90 - 40 = 50 m and
    (s-c) = 90 - 80 = 10 m

    ∴ Area of Δ ABC =
    √s(s-a)(s-b)(s-c)
    = √90 x 30 x 50 x 10 m2
    = 300√15 m2

    ∴ Area of parallelogram ABCD = 2 x area of Δ ABC
    = 600√15 m2