Here we can see that the line $h$ dissects the triangle into two smaller right-angular triangles and we know that for each of them we can calculate the
area and then sum them together. Let's take the bases to be $b1$ and $b2$ where $b = b1 + b2$ then:
Here we can see that the line $h$ dissects the triangle into two smaller right-angular triangles and we know that for each of them we can calculate the
area and then sum them together. Let's take the bases to be $b1$ and $b2$ where $b = b1 + b2$ then:
The idea is to slice $h$ up into $n$ slices and estimate the area of the slice and then add all the slices together. The bigger we make $n$ the nearer we get to the are of the triangle. $f(x)$ is
the length of the slice at the x'th slice.
Let's assume we have some arbitrary triangle and we would like to determine what is the area of a triangle is if we only know the length of it's sides. We can view it for example as follows:
We approach this from straight geometric knowledge or trigonometric knowledge.
Geometric approach
Let's start with the fact that we can determine the height of a triangle and from that and the length of the opposite side we can determine the area. Let's view above as follows:
From "Height of a Triangle we can determine the value of h, and we know the formula to determine the area of a triangle.