Areas

An area is a region surrounded by a closed curve (an entity with a continuous border, like a square, a rectangle, a triangle, or a circle).

Area of Rectangles and Squares

A rectangle is a region with four sides and four 90-degree angles. The two length sides (long sides) have equal measurements, and the two width sides (short sides) are equal to each other as well.

The area formula for a rectangle is length multiplied by width.

Area = Length × Width

A = L × W

A square is a special rectangle that has four equal sides; it is the only rectangle where the length and width are the same.

To figure the area of a square, you use the formula for the area of a rectangle: A = L × W.

For square, L = W. So,

A = L × L = L2.

Area of a Parallelogram

A parallelogram is a region with four sides. The two length sides are equal to each other and the other two sides are equal to each other, which makes the opposite sides parallel to each other. 

A rectangle requires four right angles. A parallelogram doesn’t have 90-degree angles.

The formula for the area of a parallelogram is a slight variation of the formulas for squares and rectangles: You multiply the base (B) by the height (H).

Area = Base × Height

A = B × H

Area of a Trapezoid

A trapezoid is a region with four sides, but it has only one set of parallel sides (called the bases). Finding the area of a trapezoid takes a little more information than finding the area of a rectangle or a parallelogram does. You need to know the length of both of the bases (a and b) and the height (h). You calculate the average length of the two bases for a trapezoid.

In a trapezoid, area equals height times half the sum of Base a and Base b.

Area = Height × (Base a + Base b)/2

A = h × (a + b)/2

Rectangles, squares, parallelograms, and trapezoids are all quadrilaterals, which means they are four-sided polygons.

Area of a Triangle

A triangle is a three-sided figure with three angles. Area equals one-half the product of the base and the height.

Area = 1/2 × Base × Height

A = 1/2 × b × h

Area of a Circle

A circle is a curved region with an equal distance from a fixed point (the center) to any point on the edge. You need only one measurement: the radius. The radius is the distance from the center of the circle to any point on the curved edge of the circle. It is the distance halfway across a circle.

The full distance across (through the center) is called the diameter. It is twice the length of the radius, so when you know the diameter, you can easily get the radius.

In addition to the radius, you also need pi (π) to calculate a circle's area. Pi is called a mathematical constant because its value doesn't change.

π = 3.14 or 22/7

Area equals pi times the radius squared.

Area = π × radius squared

A = π × r2

Ellipse

An ellipse is like a circle. Like a circle, it’s a region surrounded by a closed curve, but it’s taller or shorter than it is wide. The formula for calculating the area of an ellipse is similar to that for a circle.

A = π × a × b

A = πab

In the formula, a is the semi-major axis and b is the semi-minor axis. The semi-major axis is one half of the major axis (the total length of the ellipse). The semi-minor axis is one half of the minor axis (the total height of the ellipse).