the diagnoal of a square has a length of 20 square root 2. what is the area of the square?

Then each side is 20. Area is ....

the answer is 10 times the square root of 2

To find the area of a square, we need to know the length of one side. However, in this case, we are given the length of the diagonal, which is 20√2.

To determine the length of one side, we can use the relationship between the diagonal and the sides of a square. In a square, the diagonal forms a right angle with two adjacent sides, creating a right triangle.

Let's assume that the length of one side of the square is "s." By the Pythagorean theorem, we can write the relationship between the diagonal and the sides as follows:

(diagonal)^2 = (one side)^2 + (one side)^2
(20√2)^2 = s^2 + s^2
400 * 2 = 2s^2
800 = 2s^2
s^2 = 400
s = √400
s = 20

Now that we know the length of one side is 20, we can calculate the area of the square by squaring the length of one side:

Area = (one side)^2
Area = 20^2
Area = 400

Therefore, the area of the square is 400 square units.