Heron's formula gives you the area of any triangle from just the three side lengths — no height required. Magic when you don't know which side is the base.
Heron's formula
A = √(s(s−a)(s−b)(s−c))
s = (a + b + c) / 2 is the semi-perimeter.
Try it
Triangle with sides 5, 6, 7.
s = 9. A = √(9 · 4 · 3 · 2) = √216 ≈ 14.70.
It's named after Hero of Alexandria (~60 AD) but the result was almost certainly known to Archimedes 200 years earlier.