Question

Calcular el área total del cubo si s=5√2

Answer 1

Let l the length of a side edge and d the length of diagonal of a side 
so than using sin we can writing 

sin45 = l/d

sqrt2 /2 = l/d

and given that this area s=5sqrt2 what is equal l*d so in this case there are 

l/d = sqrt2 /2
l*d = 5sqrt2   => l = 5sqrt2 /d   and this subtituted in place of l inside the first equation we get 

(5sqrt2 /d)/d = sqrt2 /2

5sqrt2 /d^2 = sqrt2 /2

10sqrt2 = d^2 *sqrt2  divide both sides by sqrt2

10 = d^2

d = sqrt10  so than d = sqrt10 result l = 5sqrt2 /sqrt10 = 5sqrt20 /10 = 

= sqrt20 /2 = 2sqrt5 /2 = sqrt5

l = sqrt5
d = sqrt10

so area total del cubo = 6*l^2 = 6*(sqrt5)^2 = 6*5 = 30 unit squared 
so choice d) is right sure 

hope this will help you