## Area

Area is a quantity that is used to describe the size of a two-dimensional object in a plane. Area can also be understood as the amount of paint to cover a shape. Area can be measured by comparing it to a standard square of a fixed size. In the international system of units (SI) we call this unit the square meter. Below you can find several common methods to find the area of various shapes.

## Square

A square is a geometric shape that is a regular quadrilateral. A quadrilateral is a polygon with four edges and vertices. This simple means that it has four sides with four equal angles. It can also be said that a square is a rectangle which has two adjacent sides of equal length. To find the area of a square we just square the length.

## Rectangle

Rectangles are quadrilaterals with four right angles. Finding the area of a rectangle is very simple. All that needs to be done is to multiple the length of the rectangle by its width. The length generally refers to the longer side of the rectangle, and the width to the shorter side. If the length and width are equal then this is a special case that is called a square.

## Triangle

A triangle is a plane with three straight sides and three angles. In order to find the area of a triangle we need to first identify the information we know about the triangle(sides, angles, height, base). With this information we can then decide what equation to use to find the area. For example if we just have the sides we can use Heron's formula(also called Hero's formula) to get the area. However, if we do not know the all the side lengths then we can use additional information to choose another equation(such as the law of cosines, or the base time height equation) to find the area. Luckily for you our calculator does this for you. So all you need to do is tell it what information you have.

## Circle

A circle is a shape in which all points are the same distance from the center. This distance is called the radius. A circle can also be defined as an ellipse in which the two foci are coincident and have an eccentricity of zero. In order to find the area of a circle we use the radius and a special mathematical constant π.

## Parallelogram

The parallelogram is a quadrilateral that has two parallel sides and the other two sides have equal lengths with equal angles. To find the area of a parallelogram we simple multiple base times height.

## Trapezoid

A trapezoid is like a parallelogram in that it has two parallel sides. However, those sides don'y have to have the same length. This results in allowing the remaining two sides having different lengths and angles. In order to find the area of a trapezoid we add the top and bottom length together and then divide that result by two. Then we multiple that value by height to get the area of a trapezoid.

## Ellipse (Oval)

An ellipse (also called an oval) is similar to a circle. In an ellipse there are two focal points, and the sum of the distance to those two points is constant everywhere on the ellipse. Ellipses have a constant called eccentricity that describes their shape. This value can range from 0 (in this case it is a circle) to 1. In order to find the area of an ellipse we need its semi major axis, and semi minor axis. The semi major axis is half the height of the ellipse and half the width is the semi minor axis. The area of the ellipse is simply then the semi-major axis times the semi-minor axis times π.

## Sector

A sector is the portion of a disk that is enclosed by an arc and two radii. The length along the arc is called the arc length. The area that a sector encloses is simply going to be a partial area of a greater circle. To find it we first find the area of the circle with the radius given and then multiple that by the angle of the sector divided by either 360(or 2π if using radians).