Formulae of shapes

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

2-dimensional space

Perimeter

Cicle/spherical digon/spherical henagon

Perimeter = π × diameter.

Polygons

Perimeter = The sum of the lengths of the sides. E.g. Square = 4sides.

4*S or 4s

Area

Circle/spherical digon/spherical henagon

Area = π × radius²

Ellipse

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

Triangle

Area = Base × Height ÷ 2

Equilateral triangle

Area = $\sqrt{3}$ × side² ÷ 4

Right-angled Triangle

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

L*b

Parallelogram

Area = One side × height from that side

b*h

Trapezoid

Area = Sum of the lengths of the parallel sides × height between the parallel sides ÷ 2

(a+b)h/2

Kite or other quadrilateral with perpendicular diagonals

Area = One diagonal × the other diagonal ÷ 2

1/2*d1*d2

Bicentric quadrilateral (with both an incircle and a circumcircle)

Area = Square root of the product of the four sides

Regular Pentagon

​¹⁄₄ x √(5x(5+2x√5)) x side²

Regular polygon

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

3-dimensional space

Surface area

Sphere

Surface area = 4πr² sq.units

Cone

Curved /Lateral surface area = πrl sq.units

Total Surface area = πr(r+l) sq.units

Cylinder

Curved surface area = 2πrh sq.units

Surface area = 2πr(r+h) sq.units

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

Lateral surface area = 4(s)²

Total surface area = 6(s)²

Regular octahedron

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

Volume

Sphere

Volume = ​⁴⁄₃ π r³ cu. units

Cube

Surface area=6(a)

Cylinder

Volume = π r² h cu. units

Cube

Volume = S³ cu.units

Regular cuboid

Volume = lbh cu.units

Wedge (geometry)

$Volume=bh(\frac{a}{3}+\frac{c}{6}),$

where the base rectangle is a by b, c is the apex edge length parallel to a, and h the height from the base rectangle to the apex edge

4-dimensional space

Hypervolume

Tesseract

Hypervolume = Side⁴

References

• More Murderous Maths by Kjartan Poskitt
• Algebra And Geometry by Dan Green and Basher

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