What happens to the area of a square when its side is halved? Its area will

### Concept & Quadratic Relationship The area of a square ($A$) is equal to its side ($s$) squared ($A = s^2$). Therefore, any fractional change applied to the side is squared when determining the impact on the area. ### Step-by-Step Solution * **Step 1:** Let the original side of the square be $s$. The initial area is $A_1 = s^2$. * **Step 2:** The new side is halved, so $s_{new} = \frac{s}{2}$. * **Step 3:** The new area is $A_2 = (\frac{s}{2})^2$. * **Step 4:** Expanding this gives $A_2 = \frac{s^2}{4}$. * **Step 5:** Substituting the original area $A_1$ for $s^2$, we get $A_2 = \frac{1}{4} A_1$. * **Step 6:** This means the area becomes one-fourth of its original size. ### Exam Strategy & Shortcut Use a simple base number. Let the original side be $4$, so Area $= 16$. Halve the side to $2$, the new Area $= 4$. Since $4$ is one-fourth of $16$, the area becomes one-fourth. ### Common Pitfall The most common mistake is assuming area scales linearly and picking "become half". Always square the scaling factor for 2D measurements. ### Final Answer Therefore, the correct answer is **become one-fourth**.