What is the area of a square with a diagonal of eight times the square root of two centimeters?

To determine the area of a square when given the length of its diagonal, you can use the relationship between the diagonal and the side length of the square. For a square, the length of the diagonal (d) and the side length (s) are related by the formula:

[

d = s\sqrt{2}

]

Given that the diagonal is (8\sqrt{2}) centimeters, we can set up the equation:

[

8\sqrt{2} = s\sqrt{2}

]

To find the side length (s), we can divide both sides by (\sqrt{2}):

[

s = 8 \text{ centimeters}

]

Now that we have the side length, we can calculate the area (A) of the square using the formula for the area of a square:

[

A = s^2

]

Substituting the value of (s):

[

A = 8^2 = 64 \text{ square centimeters}

]

Thus, the area of the square is 64 square centimeters. This demonstrates the correct connection between the diagonal and the area, leading to the conclusion of 64 square centimeters being the proper