Question

explore the relationship between the radius and area of a circle by following these steps.

1. the height of the parallelogram is r.
2. the formula for the circumference of the circle is 2πr.
3. the base of the parallelogram - like figure is half the circumference of the circle, or

$b = \frac{1}{2}(2\pi r)=\pi r$
therefore, the area of the figure will be $a = \square$
options: $\pi r$, $(r)(2\pi r)$, $(r)(\pi r)$

Explanation:

Step1: Recall area of parallelogram

The area of a parallelogram is given by \( A = \text{base} \times \text{height} \).

Step2: Identify base and height

From the problem, the base \( b \) of the parallelogram - like figure is \( \pi r \) (from \( b=\frac{1}{2}(2\pi r)=\pi r \)) and the height (from step 4) is \( r \).

Step3: Calculate the area

Substitute the base and height into the area formula of the parallelogram: \( A = b\times h=\pi r\times r=(r)(\pi r) \).

Answer:

\((r)(\pi r)\)