This is a short list of some common mathematical shapes and figures and the formulas that describe them.
Shape | Area | Perimeter/Circumference | Meanings of symbols |
---|---|---|---|
Square | [math]\displaystyle{ l^2 }[/math] | [math]\displaystyle{ 4l }[/math] | [math]\displaystyle{ l }[/math] is the length of a side |
Rectangle | [math]\displaystyle{ lb }[/math] | [math]\displaystyle{ 2(l+b) }[/math] | [math]\displaystyle{ l }[/math] is length, [math]\displaystyle{ b }[/math] is breadth |
Circle | [math]\displaystyle{ \pi r^2 }[/math] | [math]\displaystyle{ 2\pi r }[/math] or [math]\displaystyle{ \pi d }[/math] | where [math]\displaystyle{ r }[/math] is the radius and [math]\displaystyle{ d }[/math] is the diameter |
Ellipse | [math]\displaystyle{ \pi ab }[/math] | where [math]\displaystyle{ a }[/math] is the semimajor axis and [math]\displaystyle{ b }[/math] is the semiminor axis | |
Triangle | [math]\displaystyle{ \frac{bh}{2} }[/math] | [math]\displaystyle{ a+b+c }[/math] | [math]\displaystyle{ b }[/math] is base; [math]\displaystyle{ h }[/math] is height; [math]\displaystyle{ a,b,c }[/math] are sides |
Parallelogram | [math]\displaystyle{ bh }[/math] | [math]\displaystyle{ 2(a+b) }[/math] | [math]\displaystyle{ b }[/math] is base, [math]\displaystyle{ h }[/math] is height, [math]\displaystyle{ a }[/math] is side |
Trapezoid | [math]\displaystyle{ \frac{a+b}{2}h }[/math] | [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] are the bases |
This is a list of volume formulas of basic shapes:[4](pp405–406)
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables
Surface area:
[math]\displaystyle{ \begin{alignat}{4} S &= 4 \pi r^2 \\[0.3ex] &= \frac{1}{\pi} C^2 \\[0.3ex] &= \sqrt[3]{\pi (6 V)^2} \\[0.3ex] \end{alignat} }[/math]
Volume:
[math]\displaystyle{ \begin{alignat}{4} V &= \frac{4}{3} \pi r^3 \\[0.3ex] &= \frac{1}{6 \pi^2} C^3 \\[0.3ex] &= \frac{1}{6 \sqrt{\pi}} S^{3/2} \\[0.3ex] \end{alignat} }[/math]
Radius:
[math]\displaystyle{ \begin{alignat}{4} r &= \frac{1}{2 \pi} C \\[0.3ex] &= \sqrt{\frac{1}{4 \pi} S} \\[0.3ex] &= \sqrt[3]{\frac{3}{4 \pi} V} \\[0.3ex] \end{alignat} }[/math]
Circumference:
[math]\displaystyle{ \begin{alignat}{4} C &= 2 \pi r \\[0.3ex] &= \sqrt{\pi S} \\[0.3ex] &= \sqrt[3]{\pi^2 6 V} \\[0.3ex] \end{alignat} }[/math]
Original source: https://en.wikipedia.org/wiki/List of formulas in elementary geometry.
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