Understanding Area in Geometry

Area is the quantity that expresses the extent of a two-dimensional figure or shape in the plane. It is the amount of space inside the boundary of a flat object.

Area is measured in square units (e.g., square centimeters cm², square meters m², square feet ft²). The formulas for calculating area vary depending on the geometric properties of the shape (e.g., number of sides, curvature).

Common Area Formulas

Square & Rectangle

Area = Width × Height

This is the simplest calculation. For a square, since all sides are equal, it is simply Side × Side or Side².

Circle

Area = π × Radius² (πr²)

Pi (π) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.

Triangle

Area = ½ × Base × Height

This applies to all triangles (right, isosceles, equilateral, scalene). The height must be the perpendicular distance from the base to the opposite vertex.

Trapezoid

Area = ½ × (Base1 + Base2) × Height

A trapezoid has two parallel sides called bases. You average the lengths of these two bases and multiply by the height.

Frequently Asked Questions

How do I calculate the area of irregular shapes?

For irregular shapes, the common method is to divide the shape into regular shapes (like squares and triangles), calculate the area of each, and add them together. Alternatively, one can use the grid method or integral calculus for precise measurements.

What is the difference between Area and Perimeter?

Area measures the space inside the shape (2D coverage). Perimeter measures the distance around the outside of the shape (the boundary length).

Can I use this for real estate?

Yes! Use the Rectangle or Square calculator to estimate the floor area of a room or lot. Just ensure you measure in consistent units (all feet or all meters).

Geometry Area Calculator