Area of a circle within a circumscribed triangle

[blueberrynerd]

If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm.

I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused as to how this answer was found. Any help would be appreciated.

 

[LCKurtz]

If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm.

I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused as to how this answer was found. Any help would be appreciated.

Of course the circle will have a $\pi$ in its area formula. For the equilateral triangle draw a line from a vertex to the center of the circle and from the center perpendicular to an adjacent side. That will give you a 30-60-90 triangle with one leg = 4. From that you can get the radius of the circle.