Geometry formulas

Geometry formulas

1. Geometry Formulas
Triangle Formula
Pythagorean Theorem
h
=s
h
1+
h

45º-45º-90º Phenomenon
23232
h=2
30º-60º-90º Phenomenon
s12
232 32
Perimeter s 1+s2+s3
Area of any Triangle


cMe
Area of Isosceles Triangle


auCe
h

Area of Right Triangle


B
PQB
he
Area of Equilateral Triangle
/
h

(

Square Formula
Perimeter 4S
Area #1 S
2

Area #2


ofy Cli a
h

Relationship between Side & Diagonal
n1
f


D = S
2

Rectangle Formula
Perimeter B=de
Area #1 BQd
Relationship between Side & Diagonal BuiC)!
h
=dy")!
h
1fy Cli a
h

Parallelogram Formula
Perimeter B=de
Area cQM
Rhombus Formula
Perimeter (n
Area #1 cQM
Area #2


"
PQ"
he

2. Trapezoid Formula
Perimeter c
P=c
h=n
P=n
h
Area


c /u
P=c /u
heQMuyC!
Circumference Formula
Circumference #1 #"
Circumference #2 #$
Diameter
%
#

Radius
%
#

Arc of Circle Formula
Arc Length (Central)
fuC$uu/&l'&%ui)$ a&(iCau
)*+
Q%
Arc Length (Inscribed)
QfuC$uu/&l'&,i/+$ysu"&(iCau
)*+
Q%

Arc of Circle Formula
Arc Measure (Intersecting Chords) [1] -.1-/1
(%0=cf0


Arc Measure (Intersecting
Secants/Tangents) [2]
-%1
(f0=cf0


Perimeter of Sector of Circle Arc Measure + 2r
A
C
D
B
P Q
A
B
C
D
1 2

3. Circle Formula
Area of Circle #1 #$
h

Area of Circle #2 #
"
h
(

Sector of Circle Formula
Area of Sector
fuC$uu/&l'&%ui)$ a&(iCau
)*+
Q($u &%y$+au
Rectangular Solids Formula
Area of Front & Back Faces BuiC)!QMuyC! e
Area of Top & Bottom Faces BuiC)!Qdy")!e
Area of Front & Back Faces dy")!QMuyC! e
Total Surface BM=Bd=dMe
Diagonal f11B
h
=d
h
=M
h

Cube Formula
Area of Cube )n
h

Volume n
2

Diagonal
f1n
n1
f


Cylinder Formula
Area of Top & Bottom Circular Bases #$
h
=#$
h
1#$
h

Lateral Surface Area #$!
Total Surface Area #$
h
=#$!
Volume #$
h
!

4. Cone Formula
Surface Area #$a=#$
h

Volume of Cone

#$
h
!
1/3 (area of Cylinder)
Sphere Formula
Surface Area (#$
h

Volume
(

#$
2

Coordinate geometry Formula
Distance 12
P32
he
h
=4
P34
he
h

Mid-point
2
P=2
h

5
4
P=4
h

e
General Form
4162=s
Slope
4
P34
h
2
P32
h