Permachart - Marketing Reference Guide: Circumscribed Circle, Trapezoidal Rule, Quadrilateral

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4 Jun 2015
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QUADRILAT E R A L S CIRCLES & CONICS
GENERAL QUADRILATERALS
Sum of the Interior Angles
A+ B+ C+ D= 360°
Perimeter a+ b+ c+ d
Area
Theorem: Diagonals of a quadrilateral with
consecutive sides a, b, c, and dare
perpendicular if and only if a2+ c2= b2+d2
Interior Angles
A= B= C= D= 90°
Perimeter
2(a+ b)
Area
ab
Sum of the Interior Angles
A+ B+ C + D= 360°, a||b
Perimeter
Area
Interior Angles
A= C, B= D
A+ B= 180°
Interior Lengths
Perimeter
2(a+ b)
Area
bh = absinA= absinB
Diameter
D= 2R
Circumference
2πR= πD
Area
Sector & Segment of Circle
Arc Length
Area
Diameter
2a= major axis
2b= minor axis
Area
πab
Perimeter
b
a
q
pc
A
B
C
D
d
θ
RECTANGLES
TRAPEZOIDS
1
2
1
4
1
44
2222
222222
2
pq b d a c
pq b d a c
sin tan
θθ
=+
=−+
DC
B
A
a
a
b
b
p
a
b
h
DC
A
θ
B
β
PARALLELOGRAMS
b
b
a
a
q
p
h
AB
C
D
CIRCLES
h
b
sector
segment
a
R
θ
s
Note: For the following figures, C= circumference and
s= arc length
PARABOLAS (SEGMENT)
B
AC
a
1/2 b
1/2 b
ELLIPSES
a
b
1
2ha b+
()
ha Aa B
pab abA
qab abB
==
=+
=+
sin sin
cos
cos
22
22
2
2
θ
θ
θθ
θ
θ
θθ
=
=
=
=−
=
=
=
=−
=
()
−−
22
2
2222
2
1
24
1
2
11
22
2
2
cos sin
sin tan
cos
sin
b
R
a
R
sR
hRb
aR b
bR R c
Rs R
R
Area (sector) = 1
2
Area (segment) = 1
2
1
216 8
416
22
222
ba
b
a
ab a
b
++ ++
ln
2
3ab
kab
a
Pb k d
ab
=
=−
=+
22
22
0
2
22
41
21
2
sin
θθ
π
π
(approximately)
Geometry
Geometry
ππ
RD
22
1
4
=
GEOMETRY A-588-61© 1997-2012 Mindsource Technologies Inc.
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