# Confusing trig shape question

• May 31st 2009, 12:44 PM
JeWiSh
Confusing trig shape question
http://i42.tinypic.com/29yh6c6.jpg

I'm really stuck here. I've tried getting the area of the sector/triangle etc. but I'm getting nowhere near that equation. Can anyone please help?
• May 31st 2009, 01:05 PM
amitface
We know the area of the sector is $\frac{\theta}{2\pi}\cdot\pi r^2$. The area of the triangle is $\frac{1}{2}r^2 \sin\theta$. (do you see why?). So the area of the shaded region is $\frac{\theta}{2\pi}\cdot\pi r^2-\frac{1}{2}r^2 \sin\theta =\frac{1}{8}\cdot s^2$, where $s$ is the length of the side of the square.

But we can find $s^2$ in terms of $r$ using Law of Cosines. $s^2=r^2+r^2-2r^2\cdot \cos\theta$.

The equation should follow with a little bit of algebra.