To find the area of a square in terms of its diagonal, we can use the relationship between the side length of the square and its diagonal.
Let’s denote the side length of the square as s. According to the properties of squares and right triangles, the diagonal d (which is given as x) can be calculated using the Pythagorean theorem:
- d = s√2
From this, we can express the side length in terms of the diagonal:
- s = d / √2
- s = x / √2
The area A of the square is given by:
- A = s²
Substituting s = x / √2 into the area formula, we get:
- A = (x / √2)²
- A = x² / 2
Therefore, the area of the square in terms of the diagonal length x is x² / 2.