How can you find the area of a square in a circle?

Let square ABCD be inscribed in a circle with radius r and center O.

Answer: The area of the square ABCD is 2r².

Let's solve it step by step.

Explanation:

As given in the above figure, square ABCD is inscribed in a circle with radius 'r' and centre 'O'

Let the sides of the square be 'a'. So, area of the square ABCD will be (side)².

The diameter of the circle is the diagonal of the square.

⇒ BD = 2r or D (diameter)

Using pythagoras theorem for triangle ABD,

⇒ (AB)² + (AD)² = (BD)²

⇒ a² + a²  = D² 

⇒ 2a²  = D² 

⇒ a = D / √ 2

⇒ a = 2r / √ 2

Area of square is a² = (2r / √ 2)²

⇒ a² = (4r² / 2)

⇒ a² = 2 r²

Thus, the area of the square ABCD in the circle is 2 r².