Question

Find the area of the equilateral triangle

Answer 1

Is there supposed to be a picture of the triangle?

Answer 2

Explanation:

Suppose that the side length is s. Imagine that one side is level. Draw a vertical line through the top vertex perpendicular to the base (level side). Label this vertical line "h." Then h and s are related as follows:

√3 h

sin 60 degrees = ------- = --------

2 s

s√3

and so h = the height of the triangle = -----------

2

The area of this triangle is (1/2)(base)(height), which here is:

(1/2)(s/2)( s√3 /2), or

(s^2)√3

A = ---------------

8