Using the concept of an equilateral triangle, it is found that it's area is given by:
[tex]A = \frac{\sqrt{3}}{4}x^2[/tex]
The height is one side of a right triangle, in which the other side is half the base and the other is the base, thus, applying the Pythagorean Theorem:
[tex]h^2 + (\frac{x}{2})^2 = x^2[/tex]
[tex]h^2 + \frac{x^2}{4} = x^2[/tex]
[tex]h^2 = \frac{3x^2}{4}[/tex]
[tex]h = \sqrt{\frac{3x^2}{4}}[/tex]
[tex]h = \frac{\sqrt{3}}{2}x[/tex]
Then, the area is:
[tex]A = \frac{bh}{2} = \frac{1}{2} \times x \times \frac{\sqrt{3}}{2}x = \frac{\sqrt{3}}{4}x^2[/tex]
A similar problem is given at https://brainly.com/question/21132291
