SOLUTION: how i can calculate area of quadrilateral having unequal four side with known diagonal. Sides: 33,40,45 & 65 Diagonal:72

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Question 945160: how i can calculate area of quadrilateral having unequal four side with known diagonal.
Sides: 33,40,45 & 65 Diagonal:72
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I would use Heron's formula to calculate the area of each of the two triangles split from the quadrilateral by the diagonal.
Heron's formula says that the area of a triangle with sides lengths a , b , and c is
area=sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29 where
s=%28a%2Bb%2Bb%29%2F2 is the "semiperimeter".
I do not know what your quadrilateral looks like, or its area,
because I do not know what side is next to the side measuring 33 and to the same side of the diagonal.

IF the sides measuring 33 and 40 are to one side of the diagonal,
and those measuring 45 and 65 are to the other side,
the quadrilateral (with its diagonal looks like
this , or this ,
or maybe a flipped over version of one of those.
The triangles' semiperimeters are
%2833%2B40%2B72%29%2F2=72.5 and %2845%2B65%2B72%29%2F2=91 ,
and their areas are
(rounded), and
sqrt%2891%2A%2891-33%29%2A%2891-40%29%2A%2891-72%29%29=sqrt%2891%2A46%2A26%2A19%29=1438.0 (rounded).
Then, the area of the quadrilateral is
215.7%2B1438.0=1653.7 .

IF the sides measuring 33 and 45 are to one side of the diagonal,
I calculate an area of 1822.5 .

IF the sides measuring 33 and 65 are to one side of the diagonal,
I calculate an area of 1883.2 .