Follows the picture , we can see area A , B and C are square .

Call the length of the square edges of squares A, B, C in turn a, b, c

=> a = \(\sqrt{S_A}=\sqrt{100}=10\) ; b = \(\sqrt{S_B}=\sqrt{36}=6\)

Apply the Pythagoras , we have :

b² + c² = a²

c² = a² - b²

c² = 10² - 6² = 64

=> c = 8 (c can not be equal to -8 because it's the length of an edge)

=> S_C = c² = 8² = 64 (cm²)

Follow the pic of Kayasari Ryuunosuke :)

\(\Rightarrow a=\sqrt{100}=10\left(cm\right)\)

\(b=\sqrt{36}=6\left(cm\right)\)

Pythagoras \(\Rightarrow\)\(c=\sqrt{10^2-6^2}=8\left(cm\right)\)

\(\Rightarrow\)\(S_C=8^2=64\left(cm^2\right)\)

Denote the length as shown.Applying the Pythagoras theorem to the right triangle above,we have : b² + c² = a²

\(\Rightarrow S_B+S_C=S_A\Rightarrow S_C=100-36=64\) (cm²)