Question

if the area of the square inscribed in a semicircle is 2cm^2,find the area of the square inscribed in a full circle

Answer 1

If the circle has radius r and the small square has side s, then

(s/2)^2 + s^2 = r^2
s^2 = 2
so,
1/2 + 2 = r^2
r = √5/2

Now, the larger square has diagonal 2r, so its area is 2r^2 = 2*5/4 = 5/2

wow - much smaller than I expected!