How to derive the formula area of triangle=(1/2)bh?
It don’t want a derivation related to rectangle or parllelogram because its the most basic formula and even the area of rectangle was derived from this formula. So I want a real basic derivation.
It can be derived using integration
consider a line of length dl and having a small thickness dx
the triangle can be assumed to be made from n lines of variable length and thickness dx
since the area covered by line is infinitesimally small it can be assumed as small rectangle having length dl and breadth dx
now area of line = dl.dx
now area of triangle= (within limits 0 to l for dl) and (within limits 0 to h for dx) integration dl.dx
i was able to imagine upto this… this will give u the hint…
Well if you were to use the example of a right triangle with the 90 degree angle at the lower left corner then you could derive this using an integral. You would just integrate the equation of the hypotenuse from 0 to b
The equation of the hypotenuse would be y=(-h/b)x + h and when integrated it would be
(-h/2b)x^2 + hx
Then plug in your limits and you would end up with:
(-bh/2 ) + bh
This simplifies to bh/2 or 1/2*b*h
References :
It can be derived using integration
consider a line of length dl and having a small thickness dx
the triangle can be assumed to be made from n lines of variable length and thickness dx
since the area covered by line is infinitesimally small it can be assumed as small rectangle having length dl and breadth dx
now area of line = dl.dx
now area of triangle= (within limits 0 to l for dl) and (within limits 0 to h for dx) integration dl.dx
i was able to imagine upto this… this will give u the hint…
References :