Geometric figures are closed sets of points on a plane or in space that are limited by a finite number of lines. They can be linear (1D), planar (2D) or spatial (3D).
Any body that has a shape is a collection of geometric shapes.
Any figure can be described by a mathematical formula of varying degrees of complexity. Starting from a simple mathematical expression to the sum of a series of mathematical expressions.
The main mathematical parameters of geometric figures are radii, lengths of sides or edges and angles between them.
Below are the basic geometric figures most often used in applied calculations, formulas and links to calculation programs.
Linear geometric shapes
1. PointA point is the basic measurement object. The main and only mathematical characteristic of a point is its coordinate.
2. Line
A line is a thin spatial object that has a finite length and is a chain of points connected to each other. The main mathematical characteristic of a line is its length.
A ray is a thin spatial object of infinite length and representing a chain of points connected to each other. The main mathematical characteristics of the ray are the coordinate of its origin and direction.
Flat geometric shapes
1. CircleA circle is a geometric locus of points on a plane, the distance from which to its center does not exceed a given number, called the radius of this circle. The main mathematical characteristic of a circle is its radius.
2. Square
A square is a quadrilateral in which all angles and all sides are equal. The main mathematical characteristic of a square is the length of its side.
3. Rectangle
A rectangle is a quadrilateral whose angles are all 90 degrees (right). The main mathematical characteristics of a rectangle are the lengths of its sides.
4. Triangle
A triangle is a geometric figure formed by three segments that connect three points (vertices of the triangle) that do not lie on the same straight line. The main mathematical characteristics of a triangle are the lengths of the sides and height.
5. Trapezoid
A trapezoid is a quadrilateral in which two sides are parallel and the other two sides are not parallel. The main mathematical characteristics of a trapezoid are the lengths of the sides and height.
6. Parallelogram
A parallelogram is a quadrilateral whose opposite sides are parallel. The main mathematical characteristics of a parallelogram are the lengths of its sides and height. 
A rhombus is a quadrilateral that has all sides, but the angles of its vertices are not equal to 90 degrees. The main mathematical characteristics of a rhombus are the length of its side and its height.
8. Ellipse
An ellipse is a closed curve on a plane, which can be represented as an orthogonal projection of a section of the circumference of a cylinder onto a plane. The main mathematical characteristics of a circle are the length of its semi-axes.
Volumetric geometric shapes
1. BallA ball is a geometric body, which is a collection of all points in space located at a given distance from its center. The main mathematical characteristic of a ball is its radius.
A sphere is the shell of a geometric body, which is a collection of all points in space located at a given distance from its center. The main mathematical characteristic of a sphere is its radius.
A cube is a geometric body that is a regular polyhedron, each face of which is a square. The main mathematical characteristic of a cube is the length of its edge.
4. Parallelepiped
A parallelepiped is a geometric body, which is a polyhedron with six faces and each of them is a rectangle. The main mathematical characteristics of a parallelepiped are the lengths of its edges.
5. Prism
A prism is a polyhedron, two of whose faces are equal polygons lying in parallel planes, and the remaining faces are parallelograms having common sides with these polygons. The main mathematical characteristics of a prism are the base area and height.
A cone is a geometric figure obtained by combining all the rays emanating from one vertex of the cone and passing through a flat surface. The main mathematical characteristics of a cone are the radius of the base and the height.
7. Pyramid
A pyramid is a polyhedron whose base is an arbitrary polygon, and the side faces are triangles that have a common vertex. The main mathematical characteristics of a pyramid are the base area and height.
8. Cylinder
A cylinder is a geometric figure bounded by a cylindrical surface and two parallel planes intersecting it. The main mathematical characteristics of a cylinder are the base radius and height.
You can quickly perform these simple mathematical operations using our online programs. To do this, enter the initial value in the appropriate field and click the button.
This page presents all the geometric figures that are most often found in geometry to represent an object or part of it on a plane or in space.
Make sure that the body is waterproof, as the method described involves immersing the body in water.
- If the body is hollow or water can penetrate into it, you will not be able to accurately determine its volume using this method. If the body absorbs water, make sure that the water will not damage it. Do not immerse electrical or electronic items in water as this may result in electric shock and/or damage to the item itself.
If possible, seal the body in a waterproof plastic bag (after deflating it). In this case, you will calculate a fairly accurate value for the volume of the body, since the volume of the plastic bag will most likely be small (compared to the volume of the body). Find the container that holds the body whose volume you are calculating.
- If you are measuring the volume of a small object, use a measuring cup with a volume graduation (scale) printed on it. Otherwise, find a container whose volume can be easily calculated, such as a cuboid, cube, or cylinder (a glass can also be considered a cylindrical container).
Take a dry towel to place the body on after it has been removed from the water.
Fill the container with water until you can completely immerse your body, but leave enough space between the surface of the water and the top edge of the container. If the base of the body is irregularly shaped, such as rounded bottom corners, fill the container so that the surface of the water reaches the regularly shaped part of the body, such as straight rectangular sides.
Mark the water level. If it absorbs water, wait at least thirty seconds and then remove the body from the water. The water level should drop because some of the water is in the body. Remove marks (marker or tape) from the previous water level and mark the new level. Then immerse the body in the water again and leave it there.
If the body floats, attach a heavy object to it (as a sinker) and continue calculations with it. After this, repeat the calculations exclusively with the sinker to find its volume. Then subtract the volume of the sinker from the volume of the body with the sinker attached and you will find the volume of the body.
- When calculating the volume of a sinker, attach to it what you used to secure the sinker to the body in question (for example, tape or pins).
Mark the level of the water with the body immersed in it. If you are using a measuring cup, record the water level according to the scale on the glass. Now you can pull the body out of the water. You probably shouldn't leave the item underwater for more than a couple of minutes, as the water may have a negative effect on it.
Know why this method works. The change in the volume of water is equal to the volume of an irregularly shaped body. The method of measuring the volume of a body using a container of water is based on the fact that when a body is immersed in a liquid, the volume of the liquid with the body immersed in it increases by the volume of the body (that is, the body displaces a volume of water equal to the volume of this body). Depending on the shape of the water container used, there are different ways to calculate the volume of displaced water, which is equal to the volume of the body.
Find the volume using the glass measuring scale. If you used a container with a measuring scale, then you should already have two values of the water level (its volume) recorded. In this case, from the value of the volume of water with the body immersed in it, subtract the value of the volume of water before the body is immersed. You will get body volume.
Find the volume using a rectangular container. If you used a rectangular parallelepiped container, measure the distance between the two marks (the water level before the body is immersed and the water level after the body is immersed), as well as the length and width of the water container. Find the volume of displaced water by multiplying the length and width of the container, as well as the distance between the two marks (that is, you calculate the volume of a small rectangular parallelepiped). You will get body volume.
- Do not measure the height of the water container. Only measure the distance between the two marks.
- Use
– a free geometric calculator will help you calculate the area or volume of relatively simple geometric shapes in two clicks. There is no need to search for the necessary formulas and make calculations on a piece of paper. Working with the program is very simple; first you need to choose what you want to calculate: the area of the figure, the total surface area or the volume. The selected figure is displayed next to it in the window, and next to it the formula for calculating the desired value will be shown. Initially, all results are rounded to the whole part, but it is possible to change and select the required accuracy with which the results should be displayed. For this, options from one to ten decimal places are available.
What can be calculated?
- Circle – we find the circumference of a circle from a known radius, and the diameter from a known circle.
- We find the area of a circle, sector of a circle, ellipse, square, rectangle, parallelogram, triangle, trapezoid, rhombus, torus.
- Surface area - cube, prism, pyramid, cylinder, sphere, cone, torus.
- Volume of figures - cube, cuboid, prism, pyramid, cylinder, spheres, cones, torus, truncated cone, barrel.