Find the area of square inscribed in a circle of radius 8 cm.

The correct answer is: ∴ Area of the given square is 128 cm2.

i Area of a square = side2
ii. Diameter of a circle = 2 × Radius
iii. All angles in a square are equal to 90°
iv. Diagonal of a square divides it into 2 right angled triangles.
Step-by-step solution:-
Let the given question be represented by the adjacent diagram.
We can observe that-
Diameter BD of the given circle = Diagonal of the Given Square ABCD
Now, we are given that for the given circle-
Radius = 8 cm.
We know that-
   Diameter = 2 ×Radius
∴ Diameter = 2 × 8
∴ Diameter = 16 cm
For Δ ABD,
∠ BAD = 90° ................................................... (All angles of a square = 90°)
Hence, Δ ABD is a right angled triangle.
By applying Pythagorean theorem, For a right angled triangle-
Hypotenuse² = sum of the squares of the remaining 2 sides
∴          (BD)² = AB² + AD²
∴             162 = AB² + AB² .............................. (Sides of a square are equal)
∴             256 = 2AB²
∴        256 / 2 = AB²
∴             128 = AB²
i.e.            AB = √128 ..................................... (Taking square root both the sides)
∴               AB = 8 √2 cm
∴ Side of the given square = AB = 8 √2 cm ................................ (Equation i)
Area of square = side2
∴ Area of square = AB2
∴ Area of square = (8 √2)2 .......................................... (From Equation i)
∴ Area of square = 64 × 2
∴ Area of square = 128 cm2
Final Answer:-
∴ Area of the given square is 128 cm2.