$$B=8·\frac{a·h}{2}$$

$$tg 22,5°=\frac{{\displaystyle \frac{a}{2}}}{h}$$

$$h=\frac{{\displaystyle \frac{a}{2}}}{tg 22,5°}=\frac{a}{2·tg 22,5°}=\frac{a}{2}·ctg 22,5°$$

$$ct{g}^2 22,5°=\frac{1+\cos 45°}{\sin 45°}$$

$$ct{g}^2 22,5°=\frac{1+{\displaystyle \frac{\sqrt{2}}{2}}}{{\displaystyle \frac{\sqrt{2}}{2}}}$$

$$ct{g}^2 22,5°=\frac{{\displaystyle \frac{2+\sqrt{2}}{\bcancel{2}}}}{{\displaystyle \frac{\sqrt{2}}{\bcancel{2}}}}$$

$$ct{g}^2 22,5°=\frac{2+\sqrt{2}}{\sqrt{2}} ·|\frac{\sqrt{2}}{\sqrt{2}}$$

$$ct{g}^2 22,5°=\frac{\left(2+\sqrt{2}\right)·\sqrt{2}}{2}$$

$$ct{g}^2 22,5°=\frac{2\sqrt{2}+2}{2}$$

$$ct{g}^2 22,5°=\frac{\bcancel{2}\left(\sqrt{2}+1\right)}{\bcancel{2}}$$

$$ct{g}^2 22,5°=\sqrt{2}+1$$

$$h=\frac{a}{2}\left(\sqrt{2}+1\right)$$

$$B=8·\frac{a·h}{2}=8·\frac{a·a}{2·2}\left(\sqrt{2}+1\right)$$

$$B=2a^2\left(\sqrt{2}+1\right)$$

$$V=B·H=2a^2\left(\sqrt{2}+1\right)·\left(\sqrt{2}+1\right)$$

$$8=2a^2{\left(\sqrt{2}+1\right)}^2$$

$$4=a^2{\left(\sqrt{2}+1\right)}^2$$

$$a^2=\frac{{\left(\sqrt{2}+1\right)}^2}{4}$$

$$M=8·a·H$$

$$M=8·\frac{2}{\bcancel{\sqrt{2}+1}}·\bcancel{\left(1+\sqrt{2}\right)}$$