Which shape’s area is calculated using A=π r²?

• A. Rectangle
• B. Circle
• C. Triangle
• D. Trapezoid

Answer: (B)

A circle’s area uses A = π r^2 because the area of a circle depends on the radius squared and involves the constant π, which relates a circle’s size to its circumference. The radius r is the distance from the center to any point on the edge, and as you grow the radius, the area grows with the square of that radius, since every direction from the center contributes to the filled space. This is why doubling the radius makes the area increase by a factor of four.

Other shapes use different formulas that don’t involve π or r^2: a rectangle uses length × width, a triangle uses 1/2 × base × height, and a trapezoid uses 1/2 × (sum of the parallel sides) × height. Because only a circle’s area is given by π r^2, the shape described by that formula is the circle.