Question

question 1 of 33
below is the justification for the formula for area of a circle. which word, when placed in the blank, best completes this argument?
the circumference of a circle is given by the formula c = 2πr where r is the radius.
if the circle is divided into equally sized sectors, the sectors can be rearranged to form a shape that approximates a parallelogram.
the base of the parallelogram is half the circumference, or πr, and the height is ____.
because the area of a parallelogram is equal to the product of the base and the height, the area is πr².
therefore, the area of a circle is given by the formula πr².

Explanation:

Step1: Recall the circle - to - parallelogram transformation

When a circle is divided into sectors and rearranged into a parallelogram - like shape, the base of the parallelogram is half of the circumference ($\pi r$).

Step2: Identify the height of the parallelogram

The height of the parallelogram formed from the circle's sectors is equal to the radius $r$ of the circle. This is because the radius of the circle is the distance from the center of the circle to the edge, and in the transformation, this distance corresponds to the height of the parallelogram - like shape.

Answer:

$r$