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

Illustrated overview of all geometric solids with important properties as well as formulas for areas, volumes and other quantities.

Mathematical basics to be able to do physics.

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

Illustrated overview of all geometric solids with important properties as well as formulas for areas, volumes and other quantities.

## Related formulas

Formula ## Circle (Area)

`$$ A ~=~ \pi \, r^2 $$`Formula ## Isosceles Triangle (Area, Base, Height)

`$$ A ~=~ \frac{1}{2} a \, \class{red}{h} $$`Formula ## Rhombus (Area, Diagonal Length)

`$$ A ~=~ \frac{1}{2} \, \class{blue}{d_1} \, \class{red}{d_2} $$`Formula ## Parallelogram (Area, Side Length)

`$$ A ~=~ \class{blue}{a} \, \class{red}{h} $$`Formula ## Trapezoid (Area, Height, Side Length)

`$$ A ~=~ \frac{1}{2} \, (a ~+~ b) \, h $$`Formula ## Trapezoid (Height, Angle)

`$$ \class{green}{h} ~=~ c \, \sin(\alpha) $$`Formula ## Sphere (Surface Area, Radius)

`$$ A ~=~ 4\pi \, \class{red}{r}^2 $$`Formula ## Sphere (Volume)

`$$ V ~=~ \frac{4}{3} \, \pi \, r^3 $$`Formula ## Ellipsoid (Volume, Semi-Axis)

`$$ V ~=~ \frac{4\pi}{3} \, a \, b \, c $$`Formula ## Torus (Surface Area, Radius)

`$$ A ~=~ 4\pi^2 \, r \, R $$`Formula ## Torus (Volume, Radius)

`$$ V ~=~ 2\pi^2 \, r^2 \, R $$`Formula ## Cube (Area, Side length)

`$$ A ~=~ 6a^2 $$`Formula ## Cube (Volume, Side Length)

`$$ V ~=~ a^3 $$`Formula ## Cuboid (Area, Side Length)

`$$ A ~=~ 2(a\,b ~+~ a\,c ~+~ b\,c) $$`Formula ## Cuboid (Volume, Side Length)

`$$ V ~=~ a \, b\, c $$`Formula ## Right Circular Cylinder (Area, Radius, Height)

`$$ A ~=~ 2\pi \, r \, (r + \class{red}{h}) $$`Formula ## Right Circular Cylinder (Volume, Radius, Height)

`$$ V ~=~ \pi \, r^2 \, \class{red}{h} $$`Formula ## Frustum of a Right Cone (Volume, Radius, Height)

`$$ V ~=~ \frac{\pi \, h}{3} \, \left( {\class{red}{r_1}}^2 ~+~ {\class{blue}{r_2}}^2 ~+~ \class{red}{r_1} \, \class{blue}{r_2} \right) $$`Formula ## Straight Circular Frustum (Side Length, Height, Radius)

`$$ s ~=~ \sqrt{h^2 ~+~ (\class{red}{r_1} - \class{blue}{r_2})^2} $$`Formula ## Right Circular Frustum (Lateral Area, Radius, Side Length)

`$$ A_{\text m} ~=~ \pi \, s \, \left( \class{red}{r_1} ~+~ \class{blue}{r_2} \right) $$`Formula ## Circular Cone (Area, Radius, Side Length)

`$$ A ~=~ \pi \, \class{red}{r} \, (\class{red}{r} + s) $$`Formula ## Right Circular Cone (Volume)

`$$ V ~=~ \frac{\pi}{3} \, h \, r^2 $$`Formula ## Tetrahedron (Area, Side Length)

`$$ A ~=~ \sqrt{3} \, a^2 $$`Formula ## Tetrahedron (Volume, Side Length)

`$$ V ~=~ \frac{\sqrt{2}}{12} \, a^3 $$`Formula ## Octahedron (Area, Side Length)

`$$ A ~=~ 2 \sqrt{3} \, a^2 $$`Formula ## Octahedron (Volume, Side Length)

`$$ V ~=~ \frac{ \sqrt{2} }{ 3 } \, a^3 $$`Formula ## Dodecahedron (Area, Side Length)

`$$ A ~=~ 3 \, a^2 \, \sqrt{25 ~+~ 10 \, \sqrt{5}} $$`Formula ## Dodecahedron (Volume, Side Length)

`$$ V ~=~ \frac{15 ~+~ 7 \, \sqrt{5}}{4} \, a^3 $$`## Related Illustrations

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Lesson ## Set Theory: Learn Subsets, Unions, Intersections and Differences

Learn set theory in a simple way: subset, intersection, union, difference, etc. using examples and Venn diagrams.

## Related Illustrations