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Math Help - Area of Quadrilateral given diagonals and 1 side.

  1. #1
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    Area of Quadrilateral given diagonals and 1 side.

    Can some one help me out please...

    In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ?

    Im sorry if this is too simple....
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  2. #2
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    Quote Originally Posted by itsmaximhere View Post
    Can some one help me out please...

    In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ?

    Im sorry if this is too simple....
    The area (K) of a quadrilateral can be found by

     K = \dfrac{1}{2} pq \sin \theta

    the diagonals are p & q

    In this case, from the data give:
    p = 2+3 = 5 & q = 4+2 = 6

    You have given the three sides of a triangle: 2,2,3
    Use the cosine law to compute  \angle AOB = \theta

    Probably easier (since  \triangle AOB is isosceles)
     \theta = 2 \, sin^{-1} \left ( \dfrac{1.5}{2} \right)

    Compute  \theta and  \sin \theta , then plug them into the equation above.
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