# The 16 most Important Geometric Objects: Overview with Formulas and Properties

**Level 1**does not require any previous knowledge. Suitable for absolute beginners.

## Table of contents

- Circle
- Isosceles Triangle
- Rhombus
- Parallelogram
- Trapezoid Flat quadrilateral with two sides parallel to each other.
- Sphere
- Ellipsoid
- Torus
- Cube
- Cuboid A cuboid is bounded by 6 rectangles.
- Straight circular cylinder
- Straight circular truncated cone
- Straight circular cone
- Tetrahedron
- Octahedron
- Dodecahedron

## Circle

Circle with **radius** \(r\). Circles occur everywhere in physics, for example in a circular motion or when particles move in a magnetic field.

**Circle (Area)**

## Isosceles Triangle

Isosceles triangle with **base** \(a\) and **height** \(h\). An isosceles triangle has at least two sides of equal length and two equal angles.

**Isosceles Triangle (Area, Base, Height)**

## Rhombus

Rhombus with **diagonals** \(d_1\) and \(d_2\), and **side lengths** \(a\).

**Rhombus (Area, Diagonal Length)**

## Parallelogram

Parallelogram with **side lengths** \(a\) and \(b\), and corresponding **angles** \(\alpha\) and \(\beta\) and **height** \(h\).

**Parallelogram (Area, Side Length)**

## Trapezoid

A trapezoid with **height** \(h\) and **side lengths** \(a\) and \(b\) is a plane quadrilateral with two sides parallel to each other.

**Trapezoid (Area, Height, Side Length)**

**Trapezoid (Height, Angle)**

## Sphere

Sphere with **radius** \(r\) and **diameter** \(d\).

**Sphere (Surface Area, Radius)**

**Sphere (Volume)**

## Ellipsoid

Ellipsoid with three **semi-axes** \(a\), \(b\), and \(c\), which are generally of different lengths.

**Ellipsoid (Volume, Semi-Axis)**

## Torus

Torus with the **radii** \(r\) and \(R\).

**Torus (Surface Area, Radius)**

**Torus (Volume, Radius)**

## Cube

A cube has 6 sides, 12 sides of equal length and 8 edges. The **side length** is \(a\).

**Cube (Area, Side length)**

**Cube (Volume, Side Length)**

## Cuboid

A cuboid is a geometric solid bounded by 6 rectangles. A cuboid has 6 rectangular side faces that are at right angles to each other, 8 right-angled edges, and 12 sides, four of which have equal lengths and are parallel to each other.

**Cuboid (Area, Side Length)**

**Cuboid (Volume, Side Length)**

## Straight circular cylinder

A straight cylinder with a **height** \(h\) and the **radius** \(r\) of its base.

**Right Circular Cylinder (Area, Radius, Height)**

**Right Circular Cylinder (Volume, Radius, Height)**

## Straight circular truncated cone

Truncated cone with round bases. The truncated cone has **height** \(h\), **side length** \(s\), **radius** \(r_1\) of the lower circular base and **radius** \(r_2\) of the upper circular base.

**Right Circular Frustum (Lateral Area, Radius, Side Length)**

**Frustum of a Right Cone (Volume, Radius, Height)**

**Straight Circular Frustum (Side Length, Height, Radius)**

## Straight circular cone

Straight circular cone with **height** \(h\), **radius** \(r\) of circular base and **side length** \(s\).

**Circular Cone (Area, Radius, Side Length)**

**Right Circular Cone (Volume)**

## Tetrahedron

Tetrahedron (regular polyhedron, Platonic solid) with **side lengths** \(a\). A tetrahedron has 4 faces and 4 corners.

**Tetrahedron (Area, Side Length)**

**Tetrahedron (Volume, Side Length)**

## Octahedron

Octahedron with **side lengths** \(a\). An octahedron has 8 faces and 6 edges.

**Octahedron (Area, Side Length)**

**Octahedron (Volume, Side Length)**

## Dodecahedron

A dodecahedron has 12 faces, 20 edges and is one of the five Platonic solids. Its **side length** is \(a\).

**Dodecahedron (Area, Side Length)**

**Dodecahedron (Volume, Side Length)**