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.
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.A = (2πr)(r)
b.A = (2πr)(2r)
c.A =(2πr)(r)
d.A =(2πr)(r2)

Answer 1

Question:

a. A = (2πr)(r)

b. A = (2πr)(2r)

c. $A =\frac{1}{2} (2\pi r)(r)$

d. $A =\frac{1}{2} (2\pi r)(2r)$

Answer:

The correct option is $A =\frac{1}{2} (2\pi r)(r)$

Step-by-step explanation:

The formula for the area, A of a parallelogram = base, b × height, h

Therefore, since the base dimension is approximately half the perimeter of a circle, we have;

Base, b = 2·π·r × 1/2

Where the height of the parallelogram, as shown in the diagram is approximately the radius of the circle, we have;

Height, h = r

Therefore, the approximate area, A of the parallelogram is given by the following relation;

A = b × h =  2·π·r × 1/2 × r Which is the same as A = $\frac{1}{2} (2\pi r)(r)$.