Which formula is used to determine the area of a circle?

The formula to determine the area of a circle is derived from the constant π (pi) and the radius (r) of the circle. The area is calculated using the formula that states the area is equal to pi times the radius squared. This means that if you know the radius of a circle, you can square it (multiply it by itself) and then multiply by π to get the total area.

The other choices represent different measurements related to circles. For example, the formula that involves 2πr calculates the circumference, which is the distance around the circle rather than the area. The formula πd is also related to the circumference and uses the diameter instead of the radius. The last choice, r²/π, does not have a standard geometric interpretation in relation to circles and does not correspond to area, circumference, or any common circular measurement. Therefore, the area of a circle is accurately expressed only by the formula πr².