Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

C: Geometric Formulas

 

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

Table C1 - 2 Dimensions 

Name Shape Formulas
Rectangle CNX_BMath_Figure_AppD_001.jpg

Perimeter: P = \(2l + 2w\)

Area: A = \(lw\)

Square CNX_BMath_Figure_AppD_002.jpg

Perimeter: P = 4s

Area: A = s2

Triangle CNX_BMath_Figure_AppD_003.jpg

Perimeter: P = a + b + c

Area: A = \(\frac{1}{2}\)bh

Sum of Angles: A + B + C = 180°

Right Triangle CNX_BMath_Figure_AppD_004.jpg

Pythagorean Theorem: a2 + b2 = c2

Area: A = \(\frac{1}{2}\)ab

Circle CNX_BMath_Figure_AppD_005.jpg

Circumference: C = 2\(\pi\)r or C = \(\pi\)d

Area: A = \(\pi\)r2

Parallelogram CNX_BMath_Figure_AppD_006.jpg

Perimeter: P = 2a + 2b

Area: A = bh

Trapezoid CNX_BMath_Figure_AppD_007.jpg

Perimeter: P = a + b + c + B

Area: A = \(\frac{1}{2}\)(B + b)h

Table C2 - 3 Dimensions 

Name Shape Formulas
Rectangular Solid CNX_BMath_Figure_AppD_008.jpg

Volume: V = \(lwh\)

Surface Area: SA = \(2lw + 2wh + 2hl\)

Cube CNX_BMath_Figure_AppD_009.jpg

Volume: V = s3

Surface Area: SA = 6s2

Cone CNX_BMath_Figure_AppD_010.jpg

Volume: V = \(\frac{1}{3} \pi r^{2} h\)

Surface Area: SA = \(\pi r^{2} + \pi r \sqrt{h^{2} + r^{2}}\)

Sphere CNX_BMath_Figure_AppD_011.jpg

Volume: V = \(\frac{4}{3} \pi r^{3}\)

Surface Area: SA = \(4 \pi r^{2}\)

Right Circular Cylinder CNX_BMath_Figure_AppD_012.jpg

Volume: V = \(\pi r^{2} h\) 

Surface Area: SA = \(2 \pi r^{2} + 2 \pi rh\)

Contributors