Skip to main content
Mathematics LibreTexts

12.3: Geometric Formulas

  • Page ID
    7304
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

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

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

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

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

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

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

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

    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 = \(\dfrac{1}{2}\)bh

    Sum of Angles: A + B + C = 180°

    Right Triangle CNX_BMath_Figure_AppD_004.jpg

    Pythagorean Theorem: a2 + b2 = c2

    Area: A = \(\dfrac{1}{2}\)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 = \(\dfrac{1}{2}\)(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 = \(\dfrac{1}{3} \pi r^{2} h\)

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

    Sphere CNX_BMath_Figure_AppD_011.jpg

    Volume: V = \(\dfrac{4}{3} \pi r^{3}\)

    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 and Attributions


    12.3: Geometric Formulas is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.

    • Was this article helpful?