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Below is the justification for the formula for the 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 [tex]$C=2 \pi r$[/tex] where [tex]$r$[/tex] 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 [tex][tex]$\pi r$[/tex][/tex], and the height is \_\_\_\_\_.
- Because the area of a parallelogram is equal to the product of the base and the height, the area is [tex]$\pi r^2$[/tex].
- Therefore, the area of a circle is given by the formula [tex]$\pi r^2$[/tex].

Which word best completes the blank?

Sagot :

GinnyAnswer
To complete the argument correctly, the blank should be filled with the term "the radius," because the height of the parallelogram formed by rearranging the circle's sectors is equivalent to the radius of the circle. Here's the complete argument with the blank filled:

- The circumference of a circle is given by the formula [tex]\(C = 2 \pi r\)[/tex], where [tex]\(r\)[/tex] 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 [tex]\(\pi r\)[/tex], and the height is the radius.
- Because the area of a parallelogram is equal to the product of the base and the height, the area is [tex]\(\pi r \times r = \pi r^2\)[/tex].
- Therefore, the area of a circle is given by the formula [tex]\(\pi r^2\)[/tex].
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