I first posted this on my blog back in October 2023 in the post titled Short Takes. The more I’ve thought about it, it deserves to stand in its own post.
What is the most general equation for the area of a triangle?
Drag the 3 vertices of the triangle
Click on green or blue lines (above P3) to incrementally adjust the triangle Desmos graphs look best on a desktop screen.
On a small mobile device select the mobile version, use landscape mode, and (maybe) collapse the left cell functions bar.
The Desmos app verifies that the area of a triangle is width times height over two.This is subtly different wording than what is traditionally taught.Width times height over two is more general thanBase times height over two. It works even when the base is tilted. Proofhttps://khoitsmahq.firstcloudit.com/images%2Fproof_base_width.png
