Explorations in College Algebra 5th Edition Complete Guide

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, Geometric Formulas Unit Conversion Relationships
1 in 5 2.54 cm 5 0.0254 m
TWO DIMENSIONAL
1 ft 5 30.5 cm 5 0.305 m
Square: Length of one side: s
Perimeter: P 5 4s 1 yd 5 91.4 cm 5 0.914 m
Area: A 5 s2 1 mi 5 1609 m 5 1.609 km

Rectangle: Length: l; width: w 1 qt 5 946 ml 5 0.9461
Perimeter: P 5 2l 1 2w 1 oz 5 28,350 mg 5 28.35 g
Area: A 5 lw 1 lb 5 453.6 g 5 0.4536 kg
Triangles: Lengths of sides: a, b, c; base: b; height: h 1 tn 5 907 kg 5 0.907 metric tn
Perimeter: P 5 a 1 b 1 c 1 light year 5 9.46 ? 1012 km or 5.88 trillion miles
Area: A 5 (1/2)bh
Pythagorean Theorem
(for right triangles only, c is the hypotenuse): Metric Prefixes for Powers of 10
a2 1 b2 5 c2
atto- a 10218
Circle: Radius: r femto- f 10215
Diameter: d 5 2r
Circumference: C 5 2␲r 5 ␲d pico- p 10212
Area: A 5 ␲r 2 nano- n 1029
micro- m 1026
THREE DIMENSIONAL
milli- m 1023
Rectangular Solids: Length: l; width: w; height: h centi- c 1022
Volume: V 5 lwh
deci- d 1021
Surface area: S 5 2lw 1 2lh 1 2wh
(unit) 100
Sphere: Radius: r deka- da 101
Volume: V 5 (4/3)␲r3 hecto- h 102
Surface area: S 5 4␲r2
kilo- k 103
Right Circular Cylinder: Radius of base: r; height: h mega- M 106
Volume: V 5 ␲r2h giga- G 109
Surface area: S 5 2␲rh 1 2␲r2
tera- T 1012
Right Circular Cone: Radius of base: r; height: h; peta- P 1015
slant length: l exa- E 1018
Volume: V 5 (1/3)␲r2h
Thus millimeter is abbreviated mm; kilometer km; and
Surface area: S 5 ␲rl 1 ␲r megameter Mm. Abbreviations are usually not used for
deci, deka, and hecto.

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