The Bermuda Triangle. It is the site of many shipwrecks and plane disappearances. Many dispute whether this is really all that extraordinary. After all, as can be seen, it encompasses a large area. Plus it is an area that has a lot of hurricanes and other disturbances in the weather. So all the mishaps could be something weird going on or maybe not that strange at all.
As mentioned, it is a large area. How large in fact. We have the standard A = 0.5bh formula, but it isn't easily used for this. So, this is a great application of Heron's formula.
To review, for any triangle with sides a, b, and c; what is called its semiperimeter is s = (a+b+c)/2.
The area then is A = square root of (s(s-a)(s-b)(s-c))
So, lets try it out. The value of s turns out to be 1,511. Plugging the numbers for a, b, c, and s into Heron's Formula gives a value of 437,600 square miles.
Different people give differing locations for the sides and vertices of the triangle, so there will be some differences. Also, we are not taking into account the curvature of the earth. Even so, it's a nice application.
