Appendix C: Geometric Formulas

2 Dimensions

Name	Shape	Formulas
Rectangle		$\begin{array}{c}\text{Perimeter:}P=2l+2w\hfill \\ \text{Area:}A=lw\hfill \end{array}$
Square		$\begin{array}{c}\text{Perimeter:}P=4s\hfill \\ \text{Area:}A=s^2\hfill \end{array}$
Triangle		$\begin{array}{c}\text{Perimeter:}P=a+b+c\hfill \\ \text{Area:}A=\frac{1}{2}bh\hfill \\ \text{Sum of Angles:}A+B+C=\text{180°}\hfill \end{array}$
Right Triangle		$\begin{array}{}\\ \text{Pythagorean Theorem:}{a}^2+b^2=c^2\hfill \\ \text{Area:}A=\frac{1}{2}ab\hfill \end{array}$
Circle		$\begin{array}{cc}\hfill & C=2\pi r\hfill \\ \text{Circumference:}\hfill & \hfill \text{or}\hfill \\ \hfill & C=\pi d\hfill \\ \text{Area:}A=\pi r^2\hfill & \hfill \end{array}$
Parallelogram		$\begin{array}{c}\text{Perimeter:}P=2a+2b\hfill \\ \text{Area:}A=bh\hfill \end{array}$
Trapezoid		$\begin{array}{c}\text{Perimeter:}P=a+b+c+B\hfill \\ \text{Area:}A=\frac{1}{2}(B+b)h\hfill \end{array}$

3 Dimensions

Name	Shape	Formulas
Rectangular Solid		$\begin{array}{c}\text{Volume:}V=lwh\hfill \\ \text{Surface Area:}SA=2lw+2wh+2hl\hfill \end{array}$
Cube		$\begin{array}{}\\ \text{Volume:}V=s^3\hfill \\ \text{Surface Area:}SA=6s^2\hfill \end{array}$
Cone		$\begin{array}{}\\ \text{Volume:}V=\frac{1}{3}\pi r^{2}h\hfill \\ \text{Surface Area:}SA=\pi r^2+\pi r\sqrt{h^2+r^2}\hfill \end{array}$
Sphere		$\begin{array}{}\\ \text{Volume:}V=\frac{4}{3}\pi r^3\hfill \\ \text{Surface Area:}SA=4\pi r^2\hfill \end{array}$
Right Circular Cylinder		$\begin{array}{}\\ \text{Volume:}V=\pi r^{2}h\hfill \\ \text{Surface Area:}SA=2\pi r^2+2\pi rh\hfill \end{array}$

Adapted from Prealgebra 2e by OpenStax (openstax.org), licensed under CC BY-NC-SA 4.0. Changes were made. License: CC-BY-NC-SA-4.0.