Area of rectangle knowing diagonal and angle between diagonal and edge I found on the web that the area of a rectangle with the diagonal of length $d$,  and inner angle (between the diagonal and edge)  $\theta$ is $d^2\cos(\theta)\sin(\theta)$. However, I wasn't able to deduce it myself. I tried applying law of sines or generalised Pythagorean theorem but I couldn't derive the area using only the length of the diagonal and the angle between diagonal and edge. How might I get to this result ?

Let $ABDC$ be a rectangle, with long sides $AB$ and $CD$ of length $l$ and short sides $AC$ and $BD$ of length $w$. And let $AD$ be a diagonal with length $d$ which makes an angle $\theta$ between $CD$ and $AD$.
Note that we have $\sin{\theta} = \frac{w}{d}$ and $cos{\theta} = \frac{l}{d}$. Multiplying by $d$ on both sides for both equations gives $$w = d \sin{\theta}$$ $$l = d \cos{\theta}$$.
