Red vs Green

In the above images, the outlined figures are congruent and so area $A$ is congruent to area $B$ . Hence $B$ is congruent to $c+d$ . Because $c$ is shared by the two areas we are trying to compare, we may ignore it. Our task amounts to a comparison between the areas of isosceles triangles $e$ and $d$ . Notice the blue angles above are congruent. Each green angle above is supplementary to a blue angle. Thus the green angles are equal to each other. For that, and the congruency of the triangle's sides, we may move $e$ like so and realize that $d$ and $e$ are triangles with equal base length and height. $d$ and $e$ therefore have the same area; the red and green areas depicted in the question are equal as well.