Question 948502
The diagonal(d) of a square forms the hypotenuse of a right triangle with two of the sides as legs.  Thus:
{{{s^2+s^2=d^2}}}
{{{2s^2=d^2}}} Find the square root of each side
{{{sqrt(2)(s)=d}}} Divide each side by {{{sqrt(2)}}}
{{{s=d/sqrt(2)}}} Substitute value of diagonal
{{{s=42.5cm/sqrt(2)}}} 
Area of a square={{{s^2}}}
{{{Area=(42.5cm/sqrt(2))^2}}}={{{((42.5cm)^2)/2}}}=1806.25 sq cm/2=903.125 sq cm
ANSWER 1: Area of the square is 903.125 sq cm.
Perimeter of a square=4s={{{4(42.5cm/sqrt(2))}}}={{{170cm/sqrt(2)}}}=120.2 cm
ANSWER 2: Perimeter of the square is 120.2 cm.