How do you cut a circle into equal sections of small central angle to find the area of circle?

Answer 1

Like cutting up a round cake (each piece starting at the centre) into very thin pieces. Each piece looks very like a thin triangle. Now arrange them next to each other alternately with points up and points down. For very thin pieces it looks almost exactly a rectangle, with the short side equalling the radius, and the 2 long sides totalling the original circumference. So the length of the rectangle is half the circumference. So the area must be RxC/2. Now pi is defined by "circumference of a circle = pi x diameter" so use that in the above area formula to get area = R x pi x diameter/2. But diameter/2 is radius. So the area is pi x R x R = pi x R2.