Formula for geometrical figures
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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