Geometry

Area

Area formulas for common 2D shapes: squares, rectangles, parallelograms, trapezoids, circles, ellipses, and triangles.

Area measures the extent of a two-dimensional region in square units (square metres, square inches, and so on). The formulas below cover squares, rectangles, parallelograms, trapezoids, circles, ellipses, and triangles, each expressed in terms of the parameters that describe the figure: side, base, height, radius, or semi-axes.

Area measures a 2D region in square units.

Square

Four equal sides of length a. Area is the side squared:

Area=a^{2}

Rectangle

Sides a and b. Area is the product of the two sides:

Area=ab

Parallelgram

Base b and perpendicular height h (the distance between the base and its opposite side, not the slanted edge). Area matches a rectangle with the same base and height:

Area=bh

Trapezoid

Parallel sides b1 and b2, with h the perpendicular distance between them (not the slanted leg). Area is the average of the parallel sides times that height:

Area=\left(\frac{1}{2}\right)\left(b1+b2\right)h

Circle

Radius r is the distance from centre to edge. Area scales with the square of r; doubling the radius quadruples the area:

Area=\pi r^{2}

Ellipse

t1 and t2 are the semi-major and semi-minor axes, half the lengths of the two principal diameters. Area is π times their product. When the axes are equal this reduces to the circle formula:

Area=\pi\left(t1\times t2\right)

Triangle

Base b and perpendicular height h (dropped onto that base, not a slanted side). Area is half the base times the height. Two such triangles tile a parallelogram of area bh:

Area=\left(\frac{1}{2}\right)bh

Equilateral Triangle

All three sides equal a, all angles 60°. Perpendicular height is a√3/2, which reduces the general triangle formula to a closed form in a:

Area=\left(\frac{\sqrt{3}}{4}\right)a^{2}