How do you solve the area of a trapezoid using diagonals The height of a trapezoid is $10$ cm. The lengths of the two diagonals of the trapezoid are $30$ cm and $50$ cm. Calculate the area of the trapezoid. 
On the homework I solved this using $${D_1D_2\over 2}$$ and my teacher marked me wrong. So I don't know what I did wrong. Please help. I know I can only use the formula if the diagonals are $90$ degrees. But how do I check that ? 


The area will be $\frac12\cdot 10\cdot (y+x+y+z)=5(x+2y+z)$
Now, $(y+z)^2+10^2=50^2$ and $(x+y)^2+10^2=30^2$
$(y+z)=\sqrt{50^2-10^2} CM=20\sqrt6 CM$
$(x+y)=\sqrt{30^2-10^2} CM=20\sqrt2 CM$
SO, the area will be $5(20\sqrt2(\sqrt3+1)) CM^2$
