1. **Problem statement:** We have a square with a diagonal length of $8\sqrt{2}$ cm. We need to find the area of the shaded triangle, which is one of the four triangles formed by the two diagonals. 2. **Formula and rules:** The diagonal $d$ of a square relates to its side length $s$ by the formula: $$d = s\sqrt{2}$$ The area $A$ of the square is: $$A = s^2$$ The two diagonals divide the square into 4 equal right triangles, so the area of one triangle is: $$\frac{A}{4}$$ 3. **Find the side length $s$:** Given: $$d = 8\sqrt{2}$$ Using the diagonal formula: $$8\sqrt{2} = s\sqrt{2}$$ Divide both sides by $\sqrt{2}$: $$\frac{8\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}} = s\frac{\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}}$$ $$8 = s$$ 4. **Calculate the area of the square:** $$A = s^2 = 8^2 = 64$$ 5. **Calculate the area of the shaded triangle:** Since the diagonals divide the square into 4 equal triangles: $$\text{Area of shaded triangle} = \frac{64}{4} = 16$$ **Final answer:** The area of the shaded triangle is $16$ cm². **Answer choice:** A) 16