# What is the shape area?

In geometry, the area of a figure is one of the main numerical characteristics of a flat body. What is the area, how to determine it in various figures, as well as what properties it has - we will consider all these questions in this article.

## What is area: definition

The area of a figure is the number of unit squares in this figure; informallyspeaking, this is the size of the shape. Most often, the area of the figure is referred to as "S". It can be measured using a pallet or a planimeter. Also, the area of the figure can be calculated, knowing its basic dimensions. For example, the area of a triangle can be calculated using three different formulas:

- S = p * (p-a) * (p-b) * (p-c) ^ 1 is Heron's formula, where p is a semi-perimeter, a, b and c are the lengths of the sides of the triangle.
- S = 0.5 * b * h, where b and h are the side of the triangle and the height drawn to this side.
- S = 0.5 * a * b * sin α, where a and b are two sides of a triangle, and alpha is the angle between them.

The area of the rectangle is equal to the product of its width and its length, and the area of the circle is equal to the product of the square of the radius and the number π = 3.14.

## Square properties

- the area is equal to equal figures;
- the area is always non-negative;
- a unit of area is a square with a side equal to 1 unit of length;
- if the figure is divided into two parts, then the total area of the figure is equal to the sum of the areas of its parts;
- figures equal in area are called equal-sized;
- if one figure belongs to another figure, then the area of the first cannot exceed the area of the second.