# Common Formulas

### CIRCUMFERENCE

- Circle:
- C = πd, in which π is 3.1416 and
*d*the diameter.

### AREA

- Triangle:
- A = (ab)/2 , in which
*a*is the base and*b*the height. - Square:
- A = a
^{2}, in which*a*is one of the sides. - Rectangle:
- A = ab, in which
*a*is the base and*b*the height. - Trapezoid:
- A = (h(a + b))/2, in which
*h*is the height,*a*the longer parallel side, and*b*the shorter. - Regular pentagon:
- A = 1.720a
^{2}, in which*a*is one of the sides. - Regular hexagon:
- A = 2.598a
^{2}, in which*a*is one of the sides. - Regular octagon:
- A = 4.828a
^{2}, in which*a*is one of the sides. - Circle:
- A = πr
^{2}, in which π is 3.1416 and*r*the radius.

### VOLUME

- Cube:
- V = a
^{3}, in which*a*is one of the edges. - Rectangular prism:
- V = abc, in which
*a*is the length,*b*is the width, and*c*the depth. - Pyramid:
- V = (Ah)/3, in which
*A*is the area of the base and*h*the height. - Cylinder:
- V = πr
^{2}h, in which π is 3.1416,*r*the radius of the base, and*h*the height. - Cone:
- V = (πr
^{2}h)/3, in which π is 3.1416,*r*theradius of the base, and*h*the height. - Sphere:
- V = (4πr
^{3})/3, in which π is 3.1416 and*r*the radius.

### TEMPERATURE SCALES

- Degrees Fahrenheit to Degrees Celsius:
- T
_{C}=^{5}/9 (T_{F}– 32) - Degrees Celsius to Degrees Fahrenheit:
- T
_{F}=^{9}/5 T_{C}+ 32 - Degrees Celsius to Kelvins:
- T
_{K}= T_{C}+ 273.15

### MISCELLANEOUS

- Distance in feet traveled by falling body:
- d = 16t
^{2}, in which*t*is the time in seconds. - Speed of sound in feet per second through any given temperature of air:
- take the square root of (273 + t), in which
*t*is the temperature Centigrade, multiply it by 1087, and divide the result by 16.52. - Cost in cents of operation of electrical device:
- C = (Wtc)/1000, in which
*W*is the number of watts,*t*the time in hours, and*c*the cost in cents per kilowatt-hour. - Conversion of matter into energy (Einstein's Theorem):
- E = mc
^{2}, in which*E*is the energy in ergs,*m*the mass of the matter in grams, and*c*the speed of light in centimeters per second: (c^{2}= 9 × 10^{20})