Let's put more details in the figure to better understand the problem:
Given:
A = Side of the cube = 4 cm
B = Diagonal of the base = √(4² + 4²) = √(16 + 16) = √(32) = 4√2 cm
Connecting sides A, B and C, it appears to be a right triangle. Thus, to find C, we will be using the Pythagorean Theorem.
[tex]\text{ C}^2=A^2+B^2[/tex]
We get,
[tex]\text{ C}^2=A^2+B^2\text{ }\rightarrow\text{ C = }\sqrt[]{A^2+B^2}[/tex][tex]\text{C = }\sqrt[]{(4)^2+(4\sqrt[]{2})^2}[/tex][tex]\text{ = }\sqrt[]{16\text{ + 16(2)}}\text{ }\rightarrow\text{ }\sqrt[]{16\text{ + 32}}[/tex][tex]\text{ = }\sqrt[]{48}[/tex][tex]=\text{ }\sqrt[]{\text{ 16 x 3}}\text{ = }\sqrt[]{16}\text{ x }\sqrt[]{3}[/tex][tex]\text{ C = 4}\sqrt[]{3}[/tex]
Therefore, the measure of the red line segment is 4√3
