Deriving the area of a trapezoid by converting it into a rectangle

Question

I am learning geometry and was trying to discover myself area of a trapezoid. I know the area of rectangle is A = width * length. I learned in school how we can split a parallelogram and convert it to rectangle and thus the area of parallelogram = area of a rectangle.

Similarly I was trying to convert a trapezoid to a rectangle. Seen in below image. So shouldn't the area of trapezoid also be area of a rectangle.

Answer 1

In the figure below, your trapezoid is $ABCD$, which is clearly not isosceles. $EF$ is midway between $AD$ and $BC$. Now $AEH$ will fill in the corner at the top left and $DFG$ will fill in the corner at the top left. We now have a rectangle with height the height of the trapezoid and base that is the average of the two bases of the trapezoid, giving the traditional formula $$area=height*\frac 12(base_1 +base_2)$$