Answer:
Area = 18
Explanation:
We know that a square has side lengths of s
We can use the Pythagorean theorem to find s
a^2 + b^2 = c^2
We know that the hypotenuse or c = the length of the diagonal or 6
Substituting in what we know
s^2 + s^2 = 6^2
2s^2 = 36
Divide each side by 2
2s^2/2 = 36/2
s^2 = 18
Take the square root of each side
sqrt(s^2) = sqrt(18)
We only have to take the positive square root since it is a length
s = sqrt(9) sqrt(2)
s= 3sqrt(2)
The side length of the square is 3sqrt(2)
To find the area, we multiply the side by the side or s^2
s^2 = (3sqrt(2))^2
From above
s^2 = 18