What formula is used to calculate the area of a parabola?

The area of a parabolic segment can be calculated using the formula that involves multiplying the base (the length of the chord at the bottom of the parabolic section) by the height (the maximum vertical distance from the base to the vertex of the parabola) and then multiplying that product by 2/3. This formula effectively describes the relationship between the shape of a parabola and the dimensions you measure to attain its area.

In contrast, the option that states area equals base times height represents the formula for the area of a rectangle, which does not apply to parabolic shapes. The formula involving 1/2 base times height typically calculates the area of triangles, specifically those with a base and height, which again does not accurately represent parabolic geometry. Lastly, the formula for 3/4 base times height does not correspond to any standard calculation for the area of a parabola and lacks mathematical justification in geometry.

When calculating the area under a parabolic curve, the 2/3 factor accounts for the curvature of the parabola, distinguishing it from linear shapes, thereby providing a more accurate representation of the area contained within.