Area of Circles, Parabolas, and Ellipses The area of a circle, parabola, and ellipse is the region bounded by the curved shape of each shape. Calculating the...
The area of a circle, parabola, and ellipse is the region bounded by the curved shape of each shape. Calculating the area allows us to determine the amount of space occupied by the shape.
Circles
The area of a circle is pi (pi) times the radius squared (r^2). A circle's radius is half the length of its diameter (d), which is why pi times diameter^2 is equal to the area.
Parabolas
A parabola is a curve that is shaped like a U. The area of a parabola is pi times the coefficient of x^2, which is half the area of a circle. This is because the area of a parabola can be calculated as pi(x^2), where x is the variable that varies along the curve.
Ellipses
An ellipse is a curve that is shaped like a stretched circle. The area of an ellipse is pi times the product of the distances from the center to the foci (2a and 2b). These distances can be calculated from the major and minor axis lengths (a and b) of the ellipse.
Examples:
The area of a circle with radius 5 cm is pi(5 cm)^2 = 78.5 cm^2.
The area of a parabola with equation x^2 = 4y is pi(4).
The area of an ellipse with major axis length 10 cm and minor axis length 6 cm is pi(10 cm)(6 cm) = 314 cm^2