90°
120°
60°
150°
30°
180°
0°
330°
210°
240°
300°
270°
7 π
π 2
12
5 π 12
2 π
π
3
3
3 π
π
4
4
5 π
π
6
6
11 π
π
12
12
π
0
13 π
23 π
12
2
7 π
11 π
6
6
5 π
7 π
4
4 4 π
5 π
3
3 17 π 12
3 π 2
19 π 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
90°
120°
60°
150°
30°
180°
0°
330°
210°
240°
300°
270°
7 π
π 2
12
5 π 12
2 π
π
3
3
3 π
π
4
4
5 π
π
6
6
11 π
π
12
12
π
0
13 π
23 π
12
2
7 π
11 π
6
6
5 π
7 π
4
4 4 π
5 π
3
3 17 π 12
3 π 2
19 π 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
GE OME TRY
SQUARE
RECTANGLE
TR APEZOID
a
PAR ALLELOGR A M
a
b
a
c
h
a
d
h
a
b
b
a + b 2
A = a2
A = ab
A = h
P = 4a
P = 2a + 2b
P = a + b + c + d
P = 2a + 2b
RHOMBUS
TRIANGLE
RIGHT TRIANGLE
CIRCLE
A = bh
(PY THAGOREAN THEOREM)
d1
h
a
c
d2
r
c
b b
A =
a
1 A = b h 2
1 d d 2 1 2
RECTANGUL AR PRISM
A = pr2
P = a + b + c
a + b = c
CONE
CYLINDER
2
2
a r
c
SPHERE
r
h b
P = 2pr
2
r
h
a 1 p r 2h 3
V = abc
V =
S = 2ab + 2ac + 2bc
S = p r 2 + p r a
GOLDEN R ATIO
4 pr3 3
V = p r 2h
V =
S = 2pr(r + h)
S = 4pr2
EULER’S POLYHEDRON THEOREM
The number of faces (f), vertices (v), and edges (e) of a convex polyhedron
b
are related by the formula:
f + v = e + 2
a + b
Rhombic Dodecahedron
a e a a+b
a
a
b
φ
1.6180339887...
v
f
For the twelve basic shapes shown above, equations are given for area (A), perimeter (P), volume (V) and surface area (S).