How to find the area of a square if the diagonal is known?

If you know the diagonal of a square, then it is easy to find its area. The area of the square will be equal to the square of the diagonal divided by two. Let us prove this by denoting the diagonal by the letter c, and the side of the square by the letter a.

In this case, the area of the square will be: a * a = a ^ 2;

The length of the diagonal of a square can be expressed by the formula: c ^ 2 = a ^ 2 + a ^ 2 = 2a ^ 2;

Let us express the area of the square in terms of the square of the diagonal: a ^ 2 = c ^ 2/2;

Answer: The area of a square is equal to the square of the diagonal divided by two.