# List of formulas in elementary geometry

## Geometric shapes

This is a short list of some common mathematical shapes and figures and the formulas that describe them.

### Two-dimensional shapes

Shape Area Perimeter/Circumference
Rectangle A = l × w P = 2l + 2w
Circle A = π × $r^2$ C = 2 × π × r
Ellipse (where a is the semimajor axis and b is the semiminor axis) A = π × a × b
Triangle A = ½ × b × h P = a + b + c
Parallelogram b = base, h = height, a = side A = b × h P = 2a + 2b
Trapezoid (where a and b are the bases) A = ½(a + b) × h

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### Three-dimensional shapes

Shape Volume Surface area
Cube $V=s^3$ $6s^2$
Rectangular Prism l = length, h = height, w = width V = l × w × h S = 2lw + 2lh + 2wh
Sphere V = ($4/3$) π $r^3$ $r^2$
Right Circular Cylinder V = π × $r^2$ × h S = 2π rh + 2π $r^2$

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### LaTeX markup (for writer/editors)

#### Circle (area and circumfrence)

$C = \,2\pi r$

$A = \,\pi r^2$

$dA = \,\mathrm{d}r\,\mathrm{d}\theta$

#### Sphere (area and volume)

$A = 4\pi r^2$

$V = \frac{4}{3}\pi r^3$

$dA = r^2 \sin\theta\, d\theta\, d\phi$

$\mathrm{d}V=r^2\sin\theta\,\mathrm{d}r\,\mathrm{d}\theta\,\mathrm{d}\varphi$