video math tutor: algebra: formulas from geometry

8/14/2019 Video Math Tutor: Algebra: Formulas From Geometry

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AL G E B R AASelf-Tutorial

by

LuisAnthonyAstProfessionalMathematics Tutor

FORMULASFROM

GEOMETRY

Copyright2006All right s reserved. No par t of th is publication ma y be reproduced or tr an smitt ed in any form

or by an y mea ns, electronic or mechan ical, including ph otocopy, recordin g, or an y inform at ion

storage or retrieval system, without permission in writing of the author.

E-mail may be sent to: [email protected]


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This docum ent is inten ded to present typical form ulas from geomet ry.

Stu dent s in a lgebra or calculus (or other higher m at h classes) will

encoun ter th em wh en doing word problems. This is NOT meant as a

form al, deta iled lesson in geometr y, just an inform al r eview. No exam ples

of th e use of th e form ula s a re given, alth ough a few more det a ils will be

provided on th e video version of this Lesson.

ANGLESFTwo an gles ar e Com pl im en ta ry Angles if th e sum of th e measur es ofth eir an gles is 90.

+ = 90

FTwo an gles ar e S up p l em en t a r y Angles if th e sum of th e measur es ofth eir an gles is 180.

+ = 180

L In th e following form ula s, heightis a lso called altitude.

TRIANGLES

s1 s2

Perimeter: P = s1 + s2 + s3s3


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h = height b = base

Area:

FAn Isosceles Triangle ha s two sides tha t a re of th e same length .

FAn E qu i l a t e r a l T r i an g l e ha s all thr ee sides of th e sam e length .

Y The su m of th e measur es of th e inter ior a ngles of an y triangle is 180.

+ + = 180

FAR i gh t T r i an g l e ha s one int erior a ngle equa l to 90.

FTh e Pythagorean Theorem sta tes: For a ny right tr iangle, th e sum ofth e squa res of th e length s of th e legs is equal t o th e squa re of th e length of

th e hypotenu se.

hypotenuse

leg

leg

OR

h

b

90


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a

b

YP y t h a g or e a n T r i p le s . Here ar e some examples of combina tions of

integers th at ma ke th e Pytha gorean equa tion tr ue:

a b c

3 4 5

5 12 13

7 24 25

8 15 17

9 40 41

Y The sides of similar tr iangles ar e proport iona l.

a b d

f

c

QUADRILATERALS(Four -sided figures )

Y Square:

s

s = side d = diagona l

s s d =

Perimeter: P = 4s

s

c

e

d


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s Area:

s

Y Rectangle:

l = length w = widt h d = diagona l

Per imeter: P = 2l + 2w

w Area:

Y Parallelogram:

b b= base s = slan t h eight

s s Perimeter: P = 2b + 2s

b

h = height

Area:

b

Y Trapezoid:s2

s1 s3 Perimeter: P = s1 + s2 + s3 + s4

s4

l

l

d

l

h

ww


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b2 b1 = first base b2 = second base

h = height

Area:

b1

In calculu s, you m ay encoun ter t ra pezoids on t heir s ides:

h1 = first height h2 = second height

b = base

h 1 h 2 Area:

b

Y The su m of th e measur es of th e inter ior a ngles of an y qua drilater al is

360.

+ + + = 360

CIRCLES

r= radius d = diameter C= circum feren ce

Diameter: d = 2r Circumference: C= 2r

or C= d

r

h

d


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Area:

3.14159265358979323846264338327950288419716939937510

is the nu mber of diameters t ha t can fit on th e

circum feren ce of a circle.

an d 3.14 are typical a pproximat ions of.

SOLID FIGURESY Cube:

s = side of cube d = dia gonal of face

D = diagonal of cube

s Sur face Area :

Volume:

s

YRecta ngula r Box (or Recta ngular Pa ra llelepiped):

= length w = widt h h = height

d = dia gonal of box

Sur face Area : S A = 2( w + wh + h )

r

D

d

dh

w


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Volume:

Y Pr isms (an y kind):

h = height A = Area of th e base

Volume:

The video illustr at es oth er exam ples of prisms.

Y Pyra mids (an y kind):

h = height A = Area of th e base

Volume:

The video illustr at es oth er exam ples of pyra mids.

Y Cone (Right Circular Cone):

s = slant height h = height

r= radius

Lat era l Sur face Area (Area of cone

not coun ting t he a rea of base):

h

w

h

h

s

A

r

h

A


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Total Surface Area:

or

Volume:

Y Cylinder (Right Circula r Cylinder ):

r= radius h = height

Lat era l Sur face Area :

Tota l Su rface Area:

Volume:

h

r

h

r

r


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Y Sphere:

r= radius

Sur face Area :

Volume:

END OFLESSON

r

r

video math tutor: algebra: formulas from geometry

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