What is the area of an equilateral triangle with side length 6 inches?

Answer 1

There is a formula for the area of an equilateral triangle given its side length:

A = s²√3/4 , where s is the length of a side.

That formula is derived by dropping an altitude from a vertex. That altitude creates two congruent triangles (HL) so the base is divided into two equal segments (s/2). Those two triangles are 30-60-90 triangles, so the altitude has a length that is √3 times the short leg (s/2). So altitude = s√3/2.

The area is 1/2 bh. The base is s (one of the sides), the altitude is s√3/2, so A = 1/2 (s) (s√3/2).

Just substitute 6 for s into the area formula and simplify to find A.