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
