Heron's Formula -- from Wolfram MathWorld
There is an area of the sea known as the "Bermuda Triandle." In the Bermuda Triangle, it is rumoured that storms arrive out of nowhere, navigation equipment doesn't work correctly, and ships vanish without a trace.
The Bermuda Triangle is between Puerto Rico, Miami, and Bermuda. It should be noted that Pueto Rico and Miami are 240 kilometers apart, Miami and Bermuda are 330 kilometers apart, and Puerto Rico and Bermuda are 270 kilometers apart. The Bermuda Triangle, according to legend, is defined as the largest possible circle that fits entirely within the triangle formed by those three islands.
What is the area of the Bermuda Triangle (or circle), in square kilometers?
There is an element theorem that says,
Where r is the radius of that circle.
A is the area of triangle
s is semi-perimeter.
The perimeter is easy, 840 thus semi-perimeter is 420.
The area is calulated with Heron's Theorem:
The area of the circle is,