Solved Question of Exercise 10.1 of Class 11th Q. No. 1

Q. No 1

Draw a quadrilateral in the cartesian plane, whose vertices are
 (-4,5), (0,7), (5,-5) and (-4,-2). Also find its area.



Sol.  :
                 Given points (-4,5), (0,7), (5,-5) and (-4,-2) are plotted.They are denotted by A, B, C, and D respectively.

Now divide the quadrilateral  into two triangles as ∆ABD &
∆BDC.


      
              ar of ∆ABD = 1/2 [-4(7+2)+0.(-2-5)+(-4)(5-7)]
                                  =   1/2 [-36+8]
                                 =    -28/2
                                =      14                                 [ Since area is not -ve]




And   ar of ∆BCD   = 1/2 [0.(-5+2)+5(-2-7)-4(7+5) ]
                               
                                = 1/2 [-45-48]
                             
                              =  93/2                                       [ Since area is not -ve]
                             




Now,
      Area of quadrilateral ABCD =  Area of  ∆ABD  +  Area of  ∆BCD  

                                                    = 14+ 93/2

                                                   =  121/2

                                                   =  60.5 Sq. unites