MathematicsIf A(−5,7),B(−4,−5),C(−1,−6)   and D(4,5)  are the vertices of a quadrilateral, then find the area of the quadrilateral ABCD  .

If A(5,7),B(4,5),C(1,6)   and D(4,5)  are the vertices of a quadrilateral, then find the area of the quadrilateral ABCD  .


  1. A
    36 square units
  2. B
    72 square units
  3. C
    144 square units
  4. D
    18 square units 

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    Solution:

    Given that, the vertices A(5,7),B(4,5),C(1,6)   and D(4,5)  .
    We have to find the area of the quadrilateral.
    The area of the triangle with the coordinates ( x 1 , y 1 ),( x 2 , y 2 ),( x 3 , y 3 )   is given by the formula,
    A= 1 2 x 1 y 2 y 3 + x 2 y 3 y 1 + x 3 y 1 y 2  .
    Find the area of the triangle.
    Area of ΔABC  :
    Here,
    ( x 1 , y 1 )=(5,7) ( x 2 , y 2 )=(4,5) ( x 3 , y 3 )=(1,6)  
    1 2 x 1 y 2 y 1 + x 2 y 3 y 1 + x 3 y 1 y 2 1 2 5 5+6 +4 67 1 7+5 1 2 35  square units   Area of ΔADC  :
    Here,
    ( x 1 , y 1 )=(5,7) ( x 2 , y 2 )=(4,5) ( x 3 , y 3 )=(1,6)  
    1 2 x 1 y 2 y 1 + x 2 y 3 y 1 + x 3 y 1 y 2 1 2 5 5+6 +4 67 1 75 1 2 109 square units  
    Find the area of quadrilateral ABCD:
    Area of ΔABC+Area of ΔADC 1 2 35 + 1 2 109 1 2 144 72 square units  
    The area of the quadrilateral is 72   square units.
    Hence, option 2) is correct.
     
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