Geometry Formulas

1. Surfaces

1.1. cube = 6 a2

1.2. prism

1.2.1. (lateral area) = perimeter(b) L

1.2.2. (total area) = perimeter(b) L + 2b

1.2.3. sphere = 4 [pi] r2

2. Sinus, Cosinus, Tangens

3. Areas

3.1. square = a2

3.2. rectangle = ab

3.3. parallelogram = bh

3.4. trapezoid = h/2 (b1 + b2)

3.5. circle = pi r 2

3.6. ellipse = pi r1 r2

3.7. triangle = (1/2) b h

3.8. equilateral triangle = (1/4)sqrt(3) a2

3.9. triangle given SAS = (1/2) a b sin C

3.10. triangle given a,b,c = [sqrt][s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula)

3.11. regular polygon = (1/2) n sin(360°/n) S2

3.11.1. when n = # of sides and S = length from center to a corner

4. Volumes

4.1. cube = a3

4.2. rectangular prism = a b c

4.3. irregular prism = b h

4.4. cylinder = b h = [pi] r2 h

4.5. pyramid = (1/3) b h

4.6. cone = (1/3) b h = 1/3 [pi] r2 h

4.7. sphere = (4/3) [pi] r3

4.8. ellipsoid = (4/3) pi r1 r2 r3