Formulae of shapes

This article gives some formulae of some shapes, using words rather than symbols.

2-dimensional space

Perimeter

Circle/spherical digon/spherical henagon

Perimeter = π × diameter.

Polygons

Perimeter = The sum of the lengths of the sides.

Area

Circle/spherical digon/spherical henagon

Area = π × radius2

Ellipse

Area = Half of short axis × half of long axis × π

Triangle

Equilateral triangle
Area = \sqrt{3} × side2 ÷ 4
Right-angled
Area = One leg × the other leg ÷ 2
General
Area = Base × height ÷ 2
Numerous other formulas are given here

Quadrilateral

Square
Area = Side2
Rectangle
Area = One side × the other side
Parallelogram
Area = One side × height from that side
Trapezoid
Area = Sum of the lengths of the parallel sides × height between the parallel sides ÷ 2
Kite or other quadrilateral with perpendicular diagonals
Area = One diagonal × the other diagonal ÷ 2
Bicentric quadrilateral (with both an incircle and a circumcircle)
Area = Square root of the product of the four sides

Regular polygon

Area = Perimeter × distance from the center to a side ÷ 2

3-dimensional space

Surface area

Sphere

Surface area = 4 × radius2 × π

Cone

Surface area = π × (radius of base)2 + π × (radius of base) × height of cone

Cylinder

Surface area = 2 × π × radius × height + 2 × π × radius2

Regular tetrahedron

Surface area = \sqrt{3} × (edge length)2

Square-based pyramid

Surface area = (Side of base)2 + 2 × (side of base) × slant height

Cube

Surface area = (Side)2 × 6

Regular octahedron

Surface area = 2 × \sqrt{3} × (edge length)2

Volume

Sphere

Volume = 43 × π × radius3

Cone

Volume = 13 × π × (radius of base)2 × height

Cylinder

Volume = π × radius2 × height

Cube

Volume = Side3

Regular cuboid

Volume = The product of the three sides

4-dimensional space

Hypervolume

Tesseract

Hypervolume = Side4

References

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