Question

$find \: the \: area \: of \: a \: cube \: whose \: diagonal \: is \: 4 \sqrt{3} cm$

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Answer 1

Answer:

8√3

Step-by-step explanation:

Look at the figure, though it is not perfect.

The red lines form a right triangle..

And ∆ABC is also a right triangle

Let the sides of cube be (a)

And AE be the diagonal=4√3

By Pythagoras theorem:

In ∆ABC

a² + a²=AC²

2a²=AC²

AC=√2 a ___(i)

Now, In red triangle, ∆ACE

EC²+AC²=AE²

a²+(√2 a) ²=4√3. (from i )

3a²=4√3

a²=4√3 /3

Now,area of cube = 6 a²=6 x (4√3/3)

=8√3 cm²