Here's an example of the Triangle proof showing the unwrapping of a circle to a triangle
Pause the animation at this intermediate shape consisting of a right angle triangle and a quarter circle
The area of triangle is
$T$ = $\large \frac{1}{2}r \frac{3 \pi r}{2} = \frac{3 \pi r^2}{4}$
The area of the quarter circle is
$\large \frac{T}{3} = \frac{\pi r^2}{4}$
The total area of the shape is
$\large T + \frac{T}{3}$
Therefore
$\large \frac{3 \pi r^2}{4} + \frac{\pi r^2}{4} = \pi r^2$
Similarly for this shape
The area of triangle is
$T$ = $\large \frac{1}{2}r {\pi r} = \frac{\pi r^2}{2}$
The area of the semi circle is
$\large T = \frac{\pi r^2}{2}$
The total area of the shape is
$\large T + T$
Therefore
$\large \frac{\pi r^2}{2} + \frac{\pi r^2}{2} = \pi r^2$
Are those valid solutions?