Basic Concepts
The basic geometric figures on a plane are a point and a straight line.
And the simplest figures are a ray, a segment and a broken line. The minimum object in geometry is a point . Its peculiarity is that it has no dimensions: it has no height, length, radius. A point can only be determined by its location, which is usually denoted by one capital letter of the Latin alphabet.
A line can be made from many points, and geometric shapes can be made from several interconnected lines.
Each mathematical figure has its own value, which can be measured using formulas and attentiveness.
Area is one of the characteristics of a closed geometric figure, which gives us information about its size. S (square) - square sign.
The perimeter is usually called the length of all sides of a polygon. The perimeter is denoted by a capital Latin P.
If parameters are passed in different units of length, you need to convert all data to one unit of measurement.
Popular units for measuring area:
- square millimeter (mm2);
- square centimeter (cm2);
- square decimeter (dm2);
- square meter (m2);
- square kilometer (km2);
- hectare (ha).
Geometric bodies are a part of space that is limited by a closed surface of its outer boundary.
If all the points of a figure belong to the same plane, then it is flat .
A three-dimensional figure is a geometric figure in which all points are not on the same plane.
Examples of volumetric geometric shapes:
- ball,
- cone,
- parallelepiped,
- cylinder,
- pyramid,
- sphere.
Let's take a closer look at some figures, analyze their definitions and properties.
Rectangle
A rectangle is a quadrilateral in which all sides intersect at right angles.
Rectangle properties:
- The diagonals of a rectangle are equal and bisect at the point of intersection.
- Around a rectangle, you can describe a circle with a center at the point of intersection of its diagonals and a radius that is equal to half the diagonal.
find out the area of a rectangle :
- S = a × b, where a, b are the width and height of the rectangle.
- S = a × √(d2 - a2), where a is the known side, d is the diagonal.
A diagonal is a line segment that connects opposite vertices of a figure. It is present in all figures whose number of vertices is more than three. - S = 0.5 × d2 ×
