How to derive Equation #3 From a velocity graph

Graph #3 states  :   d= v1Δt + ½aΔt²

While looking the first time at it , it will be difficult to notice any pattern. Actually there is.

I think that equation 3 can be derived from a velocity graph like this: 

First of all as you can see the graph is divided into 2 sections yellow and red.

The same is done with the equation #3.

The yellow part will represent the area o a triangle which is  [A = bh/2],  but on the graph the equation of a triangle would look like this [d = ½(v2 - v1)Δt].  We can simplify this formula because from what we learned before we know that (v2 - v1) = [aΔt] . We end up having  ½aΔt², when we multiply  ½Δt with (aΔt), which is the second part of our equation. 

While the red part is a square. We can find its area based on the following equation: (A = lw).

On the graph this formula can be rearranged like this: (d = v1Δt),because we have to multiply v1 with (t2-t1)

We can conclude that Equation #3 is a combination of the area of a triangle and a rectangle.

When adding the 2 sides together we will get Equation #3 as a result.