Proof 2: Triangle area

Two brothers share a slice of beer cake. Its face has a rectangle-shape. They cut it from corner to corner to get two equal halves. Those two halves namely have the same height, width and sloped side. They are completely equal with the same area.

Also, they are triangles. And half the size of the original rectangle with the same height $h$ and length $l$:

$$A_{triangle}=\frac12 \underbrace{A_{rectangle}}_{hl}=\frac12hl\quad_\blacksquare$$

The area of a rectangle is inputted here.