Chapter 3 - Determinants - 3.1 The Definition of the Determinant - Problems - Page 206: 24

$(2-\sqrt{2})\pi^2$

For any matrix \[ \left[ {\begin{array}{cc} a & b \\ c & d \\ \end{array} } \right] \] the determinant equals $ad-bc$. For the matrix \[ \left[ {\begin{array}{cc} \pi & \pi^2 \\ \sqrt{2} & 2\pi \\ \end{array} } \right] \] the determinant equals $\pi(2\pi)-(\sqrt{2})(\pi^2)=(2-\sqrt{2})\pi^2$.