Find the area of the quadrilateral using the sine and cosine rules

It would be easier to explain if the vertices were labeled.

Let's call the horizontal diagonal of the kite c.  

The area of the triangle with sides triangle is given by

c itself  is given by the Law of Cosines:

At this point I'd use a variation on Heron's formula to calculate the area.  But the question says to use the sine and cosine rules so we'll do it that way.

The opposite angle, call it D, is given by the law of Cosines.  We need its sine so we don't actually have to calculate the angle:

Now the other triangle has area

So we get a total area of

the answer is a

step-by-step explanation: