Question

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which formulas can be used to find the area of a circle?
choose all that apply.
$a = \pi d$
$a = \pi (\frac{1}{2}d)^{2}$
$a = \pi (2r)^{2}$
$a = \pi r^{2}$
$a = 2\pi d$
$a = 2\pi r$

Explanation:

Step1: Recall the formula for the area of a circle

The standard formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius.

Step2: Express radius in terms of diameter

Since \(r=\frac{d}{2}\) (where \(d\) is the diameter), substituting \(r = \frac{d}{2}\) into \(A=\pi r^{2}\) gives \(A=\pi(\frac{d}{2})^{2}\).

Answer:

\(A=\pi(\frac{d}{2})^{2}\), \(A = \pi r^{2}\)