Is the area of the circle inscribed in a square of side a cm equal to \(\pi a^2\) cm²?
Step 1: A square has all sides equal. Here each side = a cm.
Step 2: An inscribed circle means the circle touches all four sides of the square from inside.
Step 3: The diameter of this circle = side of the square = a cm.
Step 4: Radius of the circle \(r = \dfrac{\text{diameter}}{2} = \dfrac{a}{2}\) cm.
Step 5: Formula for area of a circle = \(\pi r^2\). Substituting radius: \(\pi \left(\dfrac{a}{2}\right)^2 = \pi \dfrac{a^2}{4} = \dfrac{\pi a^2}{4}\) cm².
Step 6: The given claim is \(\pi a^2\) cm². But the actual area is only \(\dfrac{\pi a^2}{4}\) cm², which is one-fourth of the claim.
Final Answer: The statement is False.