Is it true to say that area of a square inscribed in a circle of diameter p cm is p² cm²? Why?

False

When the square is inscribed in the circle, the diameter of a circle is equal to the diagonal of a square but not the side of the square.

Let side of square = a

∴ p²= a² +a²

⇒ p²= 2a²

⇒ a² = p²/2

Hence area of square = a² = p²/2