What is the shape area?

Ildar Yunusov
Ildar Yunusov
July 9, 2014
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; informallyArea of ​​a trianglespeaking, 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.
  • Rectangle areaS = 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.