Area of rectangle and triangle derivation I was wondering about the derivation for the area of a triangle and the area of a rectangle. Of course, we all know them to be $\dfrac{1}{2}bh$ and $bh$ respectively, but where is the derivation of these? If we derive the rectangle one then the triangle one obviously follows, but I don't recall ever seeing a derivation for the area of a rectangle. Is it like an axiom that we don't prove?
Area is defined as the number of smallest blocks of 1 unit that are required to fill in any 2-d geometry. 
Considering that, it is very easy to prove any area formula.
One way to define area is to start with a $b \times h$ rectangle and require its area to be $bh$.  See for example https://en.wikipedia.org/wiki/Area#Formal_definition which includes:


  Every rectangle $R$ is in $M$. If the rectangle has length $h$ and breadth $k$ then $a(R) = hk$.


Then half the rectangle (a right-angled triangle) has area $\frac12 bh$.  

Any acute triangle can be split into two right-angled triangles with a perpendicular from one vertex to the opposite side (giving the perpendicular height), while an obtuse triangle may be the difference between two right-angled triangles.  

I have more on areas of triangles at http://www.se16.info/hgb/triangle.htm