General mental ability
pi (π)=3.1415926535 ...
Perimeter formula | |
| Square | 4 * side |
| Rectangle | 2 * (length + width) |
| Parallelogram | 2 * (side1 + side2) |
| Triangle | side1 + side2 + side3 |
| Regular n-polygon | n * side |
| Trapezoid | height * (base1 + base2) / 2 |
| Trapezoid | base1 + base2 + height * [csc(theta1) + csc(theta2)] |
| Circle | 2 * pi * radius |
| Ellipse | 4 * radius1 * E(k,pi/2) E(k,pi/2) is the Complete Elliptic Integral of the Second Kind k = (1/radius1) * sqrt(radius12 - radius22) |
Area formula | |
| Square | side2 |
| Rectangle | length * width |
| Parallelogram | base * height |
| Triangle | base * height / 2 |
| Regular n-polygon | (1/4) * n * side2 * cot(pi/n) |
| Trapezoid | height * (base1 + base2) / 2 |
| Circle | pi * radius2 |
| Ellipse | pi * radius1 * radius2 |
| Cube (surface) | 6 * side2 |
| Sphere (surface) | 4 * pi * radius2 |
| Cylinder (surface of side) | perimeter of circle * height |
| 2 * pi * radius * height | |
| Cylinder (whole surface) | Areas of top and bottom circles + Area of the side |
| 2(pi * radius2) + 2 * pi * radius * height | |
| Cone (surface) | pi * radius * side |
| Torus (surface) | pi2 * (radius22 - radius12) |
Volume formula | |
| Cube | side3 |
| Rectangular Prism | side1 * side2 * side3 |
| Sphere | (4/3) * pi * radius3 |
| Ellipsoid | (4/3) * pi * radius1 * radius2 * radius3 |
| Cylinder | pi * radius2 * height |
| Cone | (1/3) * pi * radius2 * height |
| Pyramid | (1/3) * (base area) * height |
| Torus | (1/4) * pi2 * (r1 + r2) * (r1 - r2)2 |
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