Hyperbola

Let $P\left(\frac{\pi}{4}\right), Q\left(\frac{5 \pi}{4}\right), R\left(\frac{3 \pi}{4}\right), T\left(\frac{7 \pi}{4}\right)$ be the points on the hyperbola $x^2-4 y^2-4=0$ in the parametric form. Then the area of the quadrilateral $P Q R T$ is (in square units)