Explanation:
if you would just maintain your natural curiosity and imaginative qualities, geometry would be the easiest of all math disciplines, because you can always "see" the things you are working with and on, almost "touch" them.
a few things you should burn into your brain though, and keep them there for the rest of your life :
Pythagoras in right-angled triangles : come on !
c² = a² + b²
c is the Hypotenuse (the baseline opposite of the 90° angle). a and b are the legs of the triangle enclosing the 90° angle.
AND : the sum of all angles in a triangle is always (ALWAYS !) 180°.
so,
in the first case
x² = 6² + 6² = 36 + 36 = 72
x = sqrt(72) = sqrt(9×4×2) = 3×2×sqrt(2) = 6×sqrt(2)
FYI this is 8.485281374...
in the second case we have to use also trigonometry, a little bit (not just geometry).
first the angle at the bottom right corner is
180 - 90 - 60 = 30° (again, because the sum of all angles is 180°).
so, 8×sqrt(3) = sin(30) × x
because the basic sine and cosine values are only for the standard circle with radius = 1. for any larger (or smaller) circle these values have to be scaled up by the actual radius, which is in our case here x.
sin(30) = 0.5
so, we get
8×sqrt(3) = x/2
16×sqrt(3) = x
FYI - that is 27.71281292...