Cut-The-Knot-Action 8!

Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/848938737954430976]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url]. [br][br][b][color=#0000ff]How can you formally prove that the [/color][color=#ff7700]area of the orange triangle[/color][color=#0000ff] is less than or equal to [/color][/b][math]\frac{1}{3}[/math][b][color=#0000ff] of the [/color][color=#666666]area of the ENTIRE TRIANGLE? [/color][/b]

Information: Cut-The-Knot-Action 8!