How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 22 units in length?
Area of triangle is
Heron's formula gives the area of a triangle with sides
Hence to determine the area of a triangle with sides of
Hence area of triangle is
Heron's formula is usually among the poorest choices. Here are some modern forms:
For a triangle with sides
The last is of course Heron.
Usually given integer sides the factored form is fast and leads to the least messy exact answer:
If we're given 2d coordinates, the Shoelace Theorem is the quickest way to the area. If we're given 3 or more dimensional coordinates, the first two forms, which rely only on squared lengths, are best.
The first form is great for deriving the special cases as well:
Equilateral triangle :
Cool. I'm not sure why they don't teach it in school.