Answer:
d
Step-by-step explanation:
An equilateral triangle can be divided into two equal triangles by any altitude. Given side length d, the base of one of the 2 triangles will be (d/2). Because the triangles are right triangles, using the pythagorean theorem, we can deduce the leg to be [tex]\sqrt{d^2-(\frac{d}{2} )^2}[/tex], which is [tex]\frac{d\sqrt{3} }{2}[/tex]. The standard area of a triangle is base times height, so the area for any equilateral triangle given a side length of d is (d/2)*[tex]\frac{d\sqrt{3} }{2}[/tex], which is [tex]\frac{d^2\sqrt{3} }{4}[/tex].
