Question

which formulas can be used to find the area of a circle?
choose all that apply.
$a = \pi(\frac{1}{2}d)^{2}$ $a = \pi(2r)^{2}$ $a = 2\pi d$ $a = \pi d$ $a = 2\pi r$ $a = \pi r^{2}$
area is in square units, so correct formulas should have the square of the radius.
$d = 2r$

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: Analyze \(A=\pi(\frac{1}{2}d)^{2}\)

Since \(d = 2r\) (diameter - radius relationship), substituting \(r=\frac{d}{2}\) into \(A = \pi r^{2}\), we get \(A=\pi(\frac{d}{2})^{2}=\pi(\frac{1}{2}d)^{2}\).

Step3: Analyze other formulas

• For \(A=\pi(2r)^{2}\), \(\pi(2r)^{2}=4\pi r^{2}

eq\pi r^{2}\).

• \(A = 2\pi d\) and \(A=\pi d\) give linear units (circumference - related, not area). \(A = 2\pi r\) is the formula for the circumference of a circle.

Answer:

\(A=\pi(\frac{1}{2}d)^{2}\), \(A = \pi r^{2}\)