Answer:
72
Step-by-step explanation:
Cut the square into two equal triangles along the diagonal
You know that half of the diagonal is 6 so multiply that by 2 to get 12 which is the hypotenuse of your triangles
Then use the pythagorean theorem to solve for the sides
a^2 + b^2 = 12^2
a^2 + b^2 = 144
Since the original shape was a square both sides a and b are equal
a^2 = b^2
a^2 + a^2 = 144
2a^2 = 144
a^2 = 144/2
a^2 = 72
a = [tex]\sqrt{72}[/tex]
Since a = b then a = [tex]\sqrt{72}[/tex] =b
Multiply both sides a and b to get the area of the square
[tex]\sqrt{72}[/tex] * [tex]\sqrt{72}[/tex] = 72
