What is the correct formula for the area of a circle?

The correct formula for the area of a circle is derived from its geometric properties, particularly involving the radius. The area (A) is directly related to the radius (r) of the circle, specifically calculated by taking the square of the radius and multiplying it by π (pi), a mathematical constant approximately equal to 3.14. This results in the formula A = πr².

This relationship comes from the definition of area in relation to how space is measured within a two-dimensional shape. For a circle, using the radius effectively captures the distance from the center to the edge, which is crucial for accurately calculating the area enclosed by the circle.

The other formulas listed pertain to different properties of circles. The formula involving 2πr calculates the circumference, which is the distance around the circle, rather than the area. The formula πd utilizes the diameter (d) of the circle, which is twice the radius, but is not a direct formula for area. The last option involving 1/2πr² is an incorrect interpretation, as it implies a division that does not apply to the area of a circle.

Therefore, A = πr² is the accurate and well-accepted formula for determining the area of a circle