General Mathematics

Mathematica Formula

1. Perimeter Formulas:

{"Perimter of Square"==4*"Side"}//N

{"Perimter of Rectangle"==2("Length"+"Width")}//N

{"Perimter of Paralleogram"==2*"Base"+2*"Height"}//N

{"Perimeter of a Triangle"=="Side 1"+"Side 2"+"Side 3"}//N

{"Perimeter of a Trapezoid"=="Side 1"+"Side 2"+"Side 3"+"Side 4"}//N

{"Circumference of a Circle"==2*π*"Radius"}//N

{"Circumference of a Circle"==π*"Diameter"}//N

{"Perimeter of a Rhombus"==4*"Side"}//N

2. Area Formulas:

{"Area of a Square"==(("Side")^2)}//N

{"Area of Rectangle"=="Length"*"Width"}//N

{"\!\(\*StyleBox[\"Area\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\" \",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"of\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\" \",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"a\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\" \",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"Parallelogram\",FontWeight->\"Plain\"]\)"=="Base"*"Height"}//N

3. Area of a Triangle Formula:

{"Area of Triangle"==(1/2)*"Base"*"Height"}//N

4. Heron’s Formula (The area of a triangle where all three sides lengths are known):

{"Area of a Triangle using Herons Formula"==(Sqrt[("Semi-Perimter (S)")("Semi-Perimter (S)"-"Side A")("Semi-Perimter (S)"-"Side B")("Semi-Perimter (S)"-"Side C")])}//N

5. Semi-Perimeter (Perimeter of triangle divided by 2):

{"Semi-Perimter (S)"==((("Side A"+"Side B"+"Side C"))/2)}//N

6. Area of a Trapezium:

{"Area of a Trapezium"==((("Base A"+"Base B"))/2)*"Height"}//N

7. Area of a Circle Formula and Sector of a Circle:

{"Area of a Circle"==π((("r")^2))}//N

{"Area of a Sector"==((("Angle of a Sector")/360))π((("r")^2))}//N

8. Area of an Ellipse and a Rhombus (or Kite) Formula:

{"Area of an Ellipse"==π*"Major Radius"*"Minor Radius"}//N

{"Area of a Rhombus"==(1/2)*"Diagonal 1"*"Diagonal 2"}//N

9. Total Surface Area of 3 Dimensional Shapes:

{"Surface Area of a Rectangular Prism"==2(("Width"*"Length")+("Height"*"Length")+("Height"*"Width"))}//N

{"Surface Area of a Cube"==6*((("Side Length")^2))}//N

{"Surface Area of a Sphere"==4*π*(("Radius")^2)}//N

{"Surface Area of a Cylinder"==(2*π*"Radius"*"Height")+(2*π*(("Radius")^2))}//N

{"Surface are of a Triangular Prism"==2*((1/2)"Base"*"Height")+"Length"("Side 1"+"Side 2"+"Side 3")}

{"Surface Area of a Cone"==(π*(("Radius")^2))+(π*"Radius"*"Slant Height")}//N

{"Surface Area of a Cone"==(π*"Radius"("Slant Height"+"Radius"))}//N

10. Surface Area of a Pyramid:

{"Surface Area of a Pyramid"==((("Length")^2))+4*((1/2)*"Base"*"Height")}//N

11. Volume Formulas:

{"Volume of a Cube"==(("Length")^3)}//N

{"Volume of a Rectangular Prism"=="Length"*"Width"*"Height"}//N

{"Volume of a Cylinder"==π*(("Radius")^2)*"Height"}//N

{"Volume of a Triangular Prism"==((1/2)*"Base"*"Height")*"Height"}//N

{"Volume of a Sphere"==(4/3)*π*(("Radius")^3)}//N

{"Volume of a Rectangular Pyramid"==(1/3)*("Length"*"Width")*"Height"}//N

{"Volume of a Cone"==(1/3)*(π*(("Radius")^2))*"Height"}//N

12. Pythagorean Formula

{(("c")^2)==(("a")^2)+(("b")^2)}//N

{(("a")^2)==(("c")^2)-(("b")^2)}//N

{"c"==(Sqrt[(("a")^2)+(("b")^2)])}//N

{"a"==(Sqrt[(("c")^2)-(("b")^2)])}//N

{"Height"==(Sqrt[(("Hypotenuse")^2)-((((("Base")/2)))^2)])}//N

{"Surface Area of a Pyramid"==((("Length")^2))+4*((1/2)*"Base"*"Height")}//N

13. 3 Dimensional Pythagorean Formula

{(("d")^2)==(("a")^2)+(("b")^2)+(("c")^2)}//N

{"d"==(Sqrt[(("a")^2)+(("b")^2)+(("c")^2)])}//N