Show that the area A of a square inscribed in a circle with radius r is A = 2r2
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Let the sides of the square is a and
radius of the circle is r
The diagonal of a square that is inscribed inside a circle will be the diameter of the circle
Hence
Diagonal of square = a√2
Diameter of circle = 2r
Therefore
a√2 = 2r
a = r√2
Area of the square = A = a²
A = a²
A = (r√2)²
A = r² * 2
A = 2r²
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