Where Does the ½ in Triangle Area Come From?

Coming soon

The video is in production. Follow along on GitHub to hear when it is out.

The idea

Take an identical triangle, turn it half a turn and fit it on, and you get a parallelogram of base times height; one triangle is exactly half of it, which is why we divide by two.

A common mix-up

Dividing by two is just a rule to memorise; and when an obtuse triangle's height falls outside it, the formula no longer works.

Where it stops working

Using an obtuse triangle's slanted side as the height gives too much; the real height lies outside the triangle, and two obtuse triangles still make a parallelogram, so it's still half.

School year

China 5