An equilateral triangle is inscribed in a circle of radius 2. What is the area of the triangle?

Question

25207 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-14T20:46:35

$3 \sqrt{3}$ $3sqrt3$

![http://madisoncollege.edu](https://useruploads.socratic.org/wnCvEZRuTNuxw1UqVRGO_fig02f01.gif)

This is the scenario you've described, in which $a = 2$ $a=2$ .

Using the properties of $30˚-60˚-90˚$ triangles, it can be determined that $h=1$ and $s/2=sqrt3$ .

Thus, $s=2sqrt3$ and the height of the triangle can be found through $a+h=2+1=3$ .

Note that the height can also be found through using $s$ and $s/2$ as a base and the hypotenuse of a right triangle where the other leg is $3$ .

Thus, $A_"triangle"=1/2bh=1/2(2sqrt3)(3)=3sqrt3$ .