Area Shape Calculator

Area of Shape

The area of a shape is the space a 2D shape fills, usually expressed in m² (square meters). One square meter is the space required by a square of which each side is 1 meter in length. Knowing the area of a shape is used in many professions to work cost-effectively. Construction workers need to know how much flooring, paint or other material is required for their project. Farmers need to know how much fertilizer is needed for their land. The price of a house is partly determined by its 2D area. In sports, the playing field usually has some required size. There are many more use cases for calculating the area of a shape. We hope this tool can help you in your endeavors.

Calculations

Circle

The area of a circle is defined by its radius. The radius of a circle can be found by drawing a straight line from the center of the circle to one of its edges and measuring its length. The formula is:

Where r is the radius.

Rectangle

A rectangle is a shape with four sides of which all corners have an angle of 90 degrees. A square is a special case of a rectangle where each side is equal in length.The formula for a rectangle is:

Triangle

A triangle is any closed shape with three corners and three straight sides. There exists many formulas to calculate its area. The correct formula depends on the information provided. This explanation covers Heron's formula, which can be used when all three side lengths are known. The formula:

Where a, b and c represent the three sides.

s is defined as follows:

Parallelogram

A parallelogram is a closed shape with four sides of which the opposite sides are the same length, but the corners need not be 90 degrees. The area of a parallelogram is defined as follows:

Where b is the length of any side, and h is the height measured from the base straight to the perpendicular side.

Trapezoid

A trapezoid is a closed shape with four sides of which the opposite sides need not be the same length. The equation to calculate the area of a trapezoid is:

Where a and b are the lengths of any parallel sides, and h is the perpendicular distance between those sides.

Ellipse

An ellipse has the shape of a symmetric ellipse. Its area is calculated as follows:

Where a is the semi-major axis (this is the length of straight line from the center to the furthers point), and b is the semi-minor axis (this is the length of straight line from the center to the closest point).

Sector

A sector has the shape of a piece taken from a pie. For ease, we assume that the pie's shape is a circle. The piece that is taken out can be any size, as long as the two cuts perfectly go from the edge to the center. The bigger piece after the cut is called the major sector, while the smaller piece is called the minor sector. The formula to calculate the area of a sector is defined like so:

Where θ is the center angle of the sector in degrees and r is the radius of the sector. The radius is the length of a straight line drawn from the center to the edge of the sector.