Question 810711
We have a square with a diagonal of 10 m.

The length of a side of the square is "s"

The Pythagorean theorem tells us that {{{s^2+s^2=10^2=100}}}

Therefore, {{{2*s^2=100}}}; {{{s^2=50}}}; {{{s=sqrt(50)}}}

Knowing the side we can figure the area as {{{s^2=(sqrt(50))^2=50}}}

We can also determine the perimeter as the sum of the length of the four sides:

Perimeter {{{P=4*s=4*sqrt(50)=4*sqrt(2*25)=4*5*sqrt(2)=20*sqrt(2)}}}