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Mathematics

Category Theory

Geometric Shapes Area Formulas

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Ellipse

$\pi a b$

Rectangle (Diagonals given)

Area cannot be determined from diagonals alone

Trapezoid

0.5 x (Base1 + Base2) x Height

Regular Pentagon

$\frac{1}{4}\sqrt{5(5+2\sqrt{5})} s^2$

Polygon

Depends on the type of polygon

Circle

$\pi r^2$

Sector of a Circle

$0.5 r^2 \theta$ (where $\theta$ is in radians)

Annulus (Ring)

$\pi (R^2 - r^2)$

Kite

0.5 x Diagonal1 x Diagonal2

Regular Hexagon

$\frac{3\sqrt{3}}{2} s^2$

Rectangle

Length x Width

Square

Side x Side or Side^2

Parallelogram

Base x Height

Equilateral Triangle

$\frac{\sqrt{3}}{4} s^2$

Triangle

0.5 x Base x Height

Rhombus

0.5 x Diagonal1 x Diagonal2

Regular Octagon

$2(1+\sqrt{2})s^2$

Cylinder's Lateral Surface Area (3D shape)

$2\pi r h$

Sphere's Surface Area (3D shape)

$4\pi r^2$

Scalene Triangle

$\sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a+b+c}{2}$ (Heron's formula)

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