List of formulas in elementary geometry

This is a short list of some common mathematical shapes and figures and the formulas that describe them. == Two-dimensional shapes == Sources: == Three-dimensional shapes == This is a list of volume formulas of basic shapes: Cone – 1 3 π r 2 h {\textstyle {\frac {1}{3}}\pi r^{2}h} , where r {\textstyle r} is the base's radius and h {\textstyle h} is the cone's height; Cube – a 3 {\textstyle a^{3}} , where a {\textstyle a} is the side's length; Cuboid – a b c {\textstyle abc} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the sides' length; Cylinder – π r 2 h {\textstyle \pi r^{2}h} , where r {\textstyle r} is the base's radius and h {\textstyle h} is the cylinder's height; Ellipsoid – 4 3 π a b c {\textstyle {\frac {4}{3}}\pi abc} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the semi-major and semi-minor axes' length; Sphere – 4 3 π r 3 {\textstyle {\frac {4}{3}}\pi r^{3}} , where r {\textstyle r} is the radius; Parallelepiped – a b c K {\textstyle abc{\sqrt {K}}} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the sides' length, K = 1 + 2 cos ⁡ ( α ) cos ⁡ ( β ) cos ⁡ ( γ ) − cos 2 ⁡ ( α ) − cos 2 ⁡ ( β ) − cos 2 ⁡ ( γ ) {\textstyle K=1+2\cos(\alpha )\cos(\beta )\cos(\gamma )-\cos ^{2}(\alpha )-\cos ^{2}(\beta )-\cos ^{2}(\gamma )} , and α {\textstyle \alpha } , β {\textstyle \beta } , and γ {\textstyle \gamma } are angles between the two sides; Prism – B h {\textstyle Bh} , where B {\textstyle B} is the base's area and h {\textstyle h} is the prism's height; Pyramid – 1 3 B h {\textstyle {\frac {1}{3}}Bh} , where B {\textstyle B} is the base's area and h {\textstyle h} is the pyramid's height; Tetrahedron – 2 12 a 3 {\textstyle {{\sqrt {2}} \over 12}a^{3}} , where a {\textstyle a} is the side's length.

Source: Wikipedia — List of formulas in elementary geometry (CC BY-SA 4.0)

List of formulas in elementary geometry

This is a short list of some common mathematical shapes and figures and the formulas that describe them. == Two-dimensional shapes == Sources: == Three-dimensional shapes == This is a list of volume formulas of basic shapes: Cone – 1 3 π r 2 h {\textstyle {\frac {1}{3}}\pi r^{2}h} , where r {\textstyle r} is the base's radius and h {\textstyle h} is the cone's height; Cube – a 3 {\textstyle a^{3}} , where a {\textstyle a} is the side's length; Cuboid – a b c {\textstyle abc} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the sides' length; Cylinder – π r 2 h {\textstyle \pi r^{2}h} , where r {\textstyle r} is the base's radius and h {\textstyle h} is the cylinder's height; Ellipsoid – 4 3 π a b c {\textstyle {\frac {4}{3}}\pi abc} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the semi-major and semi-minor axes' length; Sphere – 4 3 π r 3 {\textstyle {\frac {4}{3}}\pi r^{3}} , where r {\textstyle r} is the radius; Parallelepiped – a b c K {\textstyle abc{\sqrt {K}}} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the sides' length, K = 1 + 2 cos ⁡ ( α ) cos ⁡ ( β ) cos ⁡ ( γ ) − cos 2 ⁡ ( α ) − cos 2 ⁡ ( β ) − cos 2 ⁡ ( γ ) {\textstyle K=1+2\cos(\alpha )\cos(\beta )\cos(\gamma )-\cos ^{2}(\alpha )-\cos ^{2}(\beta )-\cos ^{2}(\gamma )} , and α {\textstyle \alpha } , β {\textstyle \beta } , and γ {\textstyle \gamma } are angles between the two sides; Prism – B h {\textstyle Bh} , where B {\textstyle B} is the base's area and h {\textstyle h} is the prism's height; Pyramid – 1 3 B h {\textstyle {\frac {1}{3}}Bh} , where B {\textstyle B} is the base's area and h {\textstyle h} is the pyramid's height; Tetrahedron – 2 12 a 3 {\textstyle {{\sqrt {2}} \over 12}a^{3}} , where a {\textstyle a} is the side's length.

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Source: Wikipedia "List of formulas in elementary geometry" · CC BY-SA 4.0

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