Area is a quantity that describes the extent of a two-dimensional shape or surface. It can be visualized as the amount of paint needed to cover a surface and is the two-dimensional counterpart to the length of a curve and the volume of a three-dimensional mass. The standard unit for area in the International System of Units (SI) is the square meter, or m^{2}. Below are equations for some common and simple shapes, along with examples of how to calculate the area of each.

- Rectangle Area: To calculate the area of a rectangle, multiply the length by the width.
- Area of a Triangle with Three Sides: Calculate it using Heron's Formula:

s(s-a)(s-b)(s-c)√

where s = (a+b+c) / 2 - Trapezoid Area: Calculate the area of a trapezoid using the following formula: (2/ (b1 + b2)) × h
- Circle Area: To calculate the area of a circle, multiply π by the radius squared.
- Sector Area: Calculate the area of a sector using the formula: (angle/360) × π × radius squared
- Ellipse Area: Calculate the area of an ellipse using the formula: Area = πab
- Parallelogram Area: Calculate the area of a parallelogram by multiplying the base by the height.

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Area is a quantity that describes the extent of a two-dimensional shape or figure in a plane. It can be visualized as the amount of paint needed to cover a surface and is the two-dimensional counterpart to the length of a curve and the volume of a three-dimensional mass. The standard unit of measurement for area in the International System of Units (SI) is the square meter, or m^{2}. Below are equations for some common and simple shapes, along with examples of how to calculate the area for each.

A rectangle is a quadrilateral with four right angles. It is one of the simplest shapes, and calculating its area requires only knowing its length and width (or being able to measure them). A rectangle is defined as a quadrilateral with four edges and vertices. In the case of a rectangle, the length usually refers to the longest edge among the four edges, while the width refers to the shorter edge between the two. When the length and width are equal, the shape is a special case of the rectangle called a square. The equation to calculate the area of a rectangle is as follows:

**Area = Length × Width**

For example, if the length of the rectangle is 10 meters and the width is 5 meters:

`Area = 10 m × 5 m = 50 m`^{2}

There are several equations to calculate the area of a triangle based on the available information. As mentioned in the above calculator, please use a triangle calculator to get more details and equations to calculate the area of a triangle, in addition to specifying the triangle's sides using any available information. In short, the equation used in the provided calculator is known as the "Heron's formula," named after Hero of Alexandria, a Greek mathematician and engineer considered by some as one of the greatest contributors in ancient times. The equation is as follows:

**Area = √s(s - x)(s - y)(s - z)**

Where:

**s = (x + y + z) / 2**

And

**x, y, z** are the sides of the triangle

For example, if you have a triangle with side lengths of 7 meters, 9 meters, and 12 meters:

`s = (7 m + 9 m + 12 m) / 2 = 14 m`

`Area = √14 × (14 - 7) × (14 - 9) × (14 - 12) = 21 m`^{2}

A circle is a simple closed shape consisting of all points in a plane that are at a given distance from a specific central point. This distance from the center to any point on the circle is called the radius. More details about circles can be found on the circle calculator page, but to calculate the area, all you need to know is the radius and understand that values in the circle are related through the mathematical constant π. The equation to calculate the area of a circle is as follows:

Area = π × (Radius)^{2}

For example, if you have a circle with a radius of 10 meters:

`Area = π × (10 m)`^{2} = 100π m^{2}

A sector in a circle is essentially a portion enclosed by two radii and an arc. Using the diameter and the angle, the area of the sector can be calculated by multiplying the area of the circle by the known angle ratio to 360° or 2π radians, as shown in the following equation:

Area = (θ / 360) × π × (Radius)² if the angle θ is in degrees

Or

Area = (θ / 2π) × π × (Radius)² if the angle θ is in radians

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A parallelogram is a simple quadrilateral containing two pairs of parallel sides, where the opposite sides and angles are equal in length and measure. The rectangle, rhombus, and square are all special cases of a parallelogram. Remember that the classification of the shape as "simple" means that the shape is not self-intersecting. A parallelogram can be divided into a right-angled triangle and a shape resembling a parallelogram. The equation to calculate the area of a parallelogram is similar to that used for a rectangle, but instead of length and width, a parallelogram uses the base and the height, where the height is the perpendicular distance between a pair of bases. Based on the figure below, the equation to calculate the area of a parallelogram is as follows:

`Area = Base × Height`

For example, if you have a parallelogram with a base of 15 meters and a height of 10 meters:

`Area = 15 m × 10 m = 150 m`^{2}