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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Geometry
4.2 Area of Quadrilateral - I

  1. Example:
    In a quadrilateral ABCD, diagonal AC = 10 cm. The lengths of perpendiculars from B and C to AC are 6 cm and 7 cm respectively. Find the area of the quadrilateral.

    Solution:
    The area of a quadrilateral ABCD = 1/2 * d(h1+h2).
    Given that,
    d = 10 cm, h1 = 6 cm and h2 = 7 cm.
    So required area = 1/2 * 10 (6+7)
    = 1/2 * 10 * 13
    = 5 * 13
    = 65 sq.cm.

  2. Example:
    In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 6 cm and 4 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 65 sq.cm.

    Solution:
    Let the length of the diagonal be 'x'.
    The area of a quadrilateral ABCD = 1/2 * d(h1+h2).
    Given that,
    h1 = 6 cm and h2 = 4 cm.
    i.e 65 = 1/2 * x (6+4),
    i.e 65 = 1/2 * x * 10,
    i.e 65 x 2 = 10x,
    i.e x = 130/10 = 13 cm.
    Hence the length of the diagonal is 13 cm.



Directions: Read the above example carefully and answer the following questions:
  • In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 15.5 cm and 12.3 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 472.6 sq.cm.

Q 1: In a quadrilateral ABCD, diagonal AC = 10 cm. The lengths of perpendiculars from B and C to AC are 5 cm and 6 cm respectively. Find the area of the quadrilateral.
65 sq.cm
60 sq.cm
50 sq.cm
55 sq.cm

Q 2: In a quadrilateral ABCD, diagonal AC = 11cm. The length of perpendicular from B to AC is 7cm. Find the length of the perpendicular from C to AC if the area of the quadrilateral is given by 88 sq.cm.
8 cm
9 cm
7 cm
6 cm

Q 3: In a quadrilateral ABCD, diagonal AC = 13 cm. The length of perpendicular from C to AC is 9 cm. Find the length of the perpendicular from B to AC if the area of the quadrilateral is given by 130 sq.cm.
11 cm
9 cm
14 cm
13 cm

Q 4: In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 5 cm and 6 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 49.5 sq.cm.
9 cm
3 cm
6 cm
4 cm

Q 5: In a quadrilateral ABCD, diagonal AC = 15 cm. The lengths of perpendiculars from B and C to AC are 6 cm and 7 cm respectively. Find the area of the quadrilateral.
97 sq.cm
87.5 sq.cm
87 sq.cm
97.5 sq.cm

Q 6: In a quadrilateral ABCD, diagonal AC = 12cm. The length of perpendicular from C to AC is 8cm. Find the length of the perpendicular from B to AC if the area of the quadrilateral is given by 90 sq.cm.
8 cm
8 cm
7 cm
12 m

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Question 8: This question is available to subscribers only!


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