1. **Problem statement:** Calculate the area of a square when its diagonal length is given as $1.6 + a$ cm. 2. **Formula used:** The area $A$ of a square with diagonal $d$ is given by $$A = \frac{d^2}{2}$$ This comes from the Pythagorean theorem since the diagonal splits the square into two right triangles. 3. **Calculation:** Substitute $d = 1.6 + a$: $$A = \frac{(1.6 + a)^2}{2}$$ 4. **Expand the square:** $$(1.6 + a)^2 = 1.6^2 + 2 \times 1.6 \times a + a^2 = 2.56 + 3.2a + a^2$$ 5. **Final expression for area:** $$A = \frac{2.56 + 3.2a + a^2}{2} = 1.28 + 1.6a + \frac{a^2}{2}$$ 6. **Explanation:** The area depends on the variable $a$ and is expressed as a quadratic function of $a$. This formula allows you to find the area for any value of $a$. **Final answer:** $$\boxed{A = 1.28 + 1.6a + \frac{a^2}{2} \text{ cm}^2}$$