Is it true to say that the area of a square inscribed in a circle of diameter \(p\) cm is \(p^2\) cm²? Why?
Step 1: A square is inscribed in a circle. This means all four vertices (corners) of the square touch the circle.
Step 2: In such a case, the diagonal of the square is equal to the diameter of the circle.
So, diagonal of the square = \(p\) cm.
Step 3: Formula for the area of a square in terms of its diagonal:
\[ \text{Area of square} = \dfrac{(\text{diagonal})^2}{2} \]
Step 4: Substitute diagonal = \(p\):
\[ \text{Area} = \dfrac{p^2}{2} \;\text{cm}^2 \]
Step 5: The statement given says the area is \(p^2\) cm². But we calculated it as \(\tfrac{p^2}{2}\) cm².
Final Answer: The statement is false. The correct area is \(\tfrac{p^2}{2}\) cm².