The cube: Surface area and volume

The cube is a figure composed by $6$ square faces, as we can see in the following picture

Calculate the diagonal $D$ of the cube of the figure if $a=10$.

If we apply the Pythagoras theorem in a square of side $10$, we can see that: $$d^2=2 \cdot a^2=200\\ d= 10 \sqrt{2}$$

Now a rectanglular triangle with legs $a$ and $d$, and hypotenuse $D$ is formed . If we apply Pythagoras again: $$D^2=d^2+a^2=(10\sqrt{2})^2+100 \\D=\sqrt{3} \cdot=17,32$$

Then, $$D=\sqrt{3} \cdot a \\ A=6 \cdot a^2 \\ V=a^3$$