A park, in the shape of a quadrilateral ABCD, has C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?


Given: The figure is given below:


 


The dimensions of the park as follows:


Angle C = 900,


AB = 9m,


BC = 12m,


CD = 5m


And, AD = 8m


Now, BD is joined.


In by Pythagoras theorem,


BD2 = BC2 + CD2


BD2 = 122 + 52


BD2 = 169


BD = 13m



Now, Semi perimeter of triangle (ABD) =


= 13/2  = 15m


Using Heron’s formula,


Area of =


=


=


=


= m2


= 35.5 m2 (approx.)


Area of quadrilateral ABCD = Area of


= 30 + 35.5


= 65.5 m2



Thus, the park acquires an area of 65.5 m2

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