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.
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.
⇒ 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.