Answer:
The surface area of the cube is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The length of a diagonal of a cube is equal to
[tex]D=b\sqrt{3}[/tex]
where
b is the length side of a cube
In this problem we have
[tex]D=12\ units[/tex]
so
[tex]12=b\sqrt{3}[/tex]
solve for b
[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]
Simplify
[tex]b=4\sqrt{3}\ units[/tex]
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
substitute the value of b
[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]
