**Perimeter, area, surface area and volume**

This animation presents the formulas to calculate the perimeter and area of shapes as well as the surface area and volume of solids.

**Mathematics**

**Keywords**

volume, surface, circumference, area, sphere, pyramid, cylinder, circle sector, circle, triangle, rectangle, square, cone, cuboid, base area, lateral surface, parallelogram, formula, geometry, solid geometry, mathematics

**Related items**

### Scenes

- trapezoid

A **two-dimensional geometric shape** is a part of a plane that is enclosed by straight or curved lines, does not contain any holes and remains intact even if one of its points is removed.

The **area** is a function that assigns a positive number to all two-dimensional geometric shapes with the following conditions:

1. The area of the unit square is 1.

2. The area of congruent geometric shapes is equal.

3. If we divide a geometric shape into several parts, the sum of the areas of the parts is equal to the area of the original geometric shape.

The area of a **rectangle** is the product of its width and height.

The area of a **triangle** is half the product of its base length and its height. (This formula derives from the formula of the area of the parallelogram.)

The area of a **parallelogram** is the product of its base length and height.

The area of a **trapezoid** is the product of half the sum of the parallel sides and its height.

The area of a **circle** can be calculated by multiplying the square of its radius with π (pi).

The area of a **circular sector** can be calculated from the area of the full circle, using the ratio of the central angle to the full angle (360°).

### Related items

#### Cube

This animation demonstrates the components (vertices, edges, diagonals and faces) of the cube, one of the Platonic solids.

#### Sphere

A sphere is the set of points which are all within the same distance from a given point in space.

#### Conic sections

The conic section is a plane curve that is created when a right circular cone is intersected by a plane.

#### Platonic solids

This animation demonstrates the five regular three-dimensional (or Platonic) solids, the best known of which is the cube.

#### Ratio of volumes of similar solids

This 3D scene explains the correlation between the ratio of similarity and the ratio of volume of geometric solids.

#### Regular square pyramid

A regular square pyramid is a right pyramid with a square base and four triangular faces.

#### Surface area of spheres (demonstration)

The surface of a sphere consists of the set of points which are all at the same distance from a given point in space.

#### Volume and surface area (exercise)

An exercise about the volume and surface area of solids generated from a ´base cube´.

#### Volume of spheres (Cavalieri´s principle)

Calculating the volume of a sphere is possible using an appropriate cylinder and cone.

#### Volume of spheres (demonstration)

The sum of the volume of the ´tetrahedrons´ gives an approximation of the volume of the sphere.

#### Cylindrical solids

This animation demonstrates various types of cylindrical solids as well as their lateral surfaces.

#### Solids of revolution

Rotating a geometric shape around a line within its geometric plane as an axis results in a solid of revolution.