# Visually prove area = 1/2 (base * height) for scalene triangle.

Please refer to image for explanation.

The area of the combined rectangle is $$(a+b)h$$ so the area of the large blue and red right-angled triangle is half this, namely $$\frac12(a+b)h$$
The area of the small rectangle on the left is $$ah$$ so the area of the small red right-angled triangle on the left is half this, namely $$\frac12ah$$
So the area of the blue triangle is the difference in area between the two right-angled triangles, namely $$\frac12(a+b)h-\frac12ah = \frac12bh$$, i.e. half of base times height