Question

The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.

A circle is shown. The circle is cut into 8 equal pieces. Pieces of the circle with radius r are rearranged to create a shape that resembles a parallelogram.

Since the circumference of the circle can be represented by 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure?

A = (2πr)(r)
A = (2πr)(2r)
A =One-half(2πr)(r)
A =One-half(2πr)(r2)

Answer 1

A = One-half(2πr)(r)

Reason: the rearranged shape has base = half the circumference = (1/2)(2πr) and height = r, so area = base·height = (1/2)(2πr)·r = πr^2.