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    Let ABCD be a quadrilateral and AC, BD be diagonals. The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8
    Question

    Let ABCD be a quadrilateral and AC, BD be diagonals. The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8 cm. Find the area of the quadrilateral ABCD (in cm²).

    A.

    140

    B.

    120

    C.

    148

    D.

    1282

    Correct option is A

    Given:
    BD = 20 cm
    Height of triangle ABD = 6 cm
    Height of triangle BCD = 8 cm
    Formula Used:
    Area of triangle = 12\frac 12​×Base×Height
    Area of quadrilateral = Sum of areas of two triangles formed by one diagonal
    Solution:
    Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD
    Area of quadrilateral ABCD = 12×20×6+12×20×8\frac12×20×6+\frac12×20×8​​
    Area of quadrilateral ABCD = 60 + 80 = 140 sq. cm.

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