A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate height of the figure when its area is 42.25 pi square centimeters.

Answer 1

A Rhombus is the largest 4 sided figure that can be circumscribed by a circle.

There isn't a proof for this that I've found, but my assumption is true in researching this.

Then a diagonal (D₁ or D₂) of the rhombus is equals 2r, where r is the radius of the circle.

The area of a rhombus is, A = D₁D₂/2 = (2r)(2r)/2 = 4r²/2 = 2r²

Since the area of a square is A=x² where x is a side of a square.

Then taking the square root of the rhombus's area, 2r², √(2r²) = r√2 which is the height of the rhombus.