Geometry Formulas
Area
of polygons:
Rectangles, Squares
A = lw
Parallelograms
A = bh
Rhombuses, Kites
A = ½d1d2
Triangles
A = ½bh
Trapezoids
A = ½h(b1 + b2)
Circles
A = p
r2
; (C = 2p
r)
Area
of
Regular polygons
A = ½ap
Sectors
A =
(x/360)
p
r2
Length of arc
L =
(x/360)
2p
r
=
(x/180)
p
r
Solids:
L.A. = Lateral Area
T.A. = Total Area or Surface Area
V = Volume
B = Area of the base
p = perimeter l
= slant height h = height
L.A.
T.A.
V
Prisms
ph
ph + 2B Bh
Cylinders
2p
rh
2p
rh + 2B
Bh
Pyramids
½pl
½pl + B
1/3Bh
Cones
prl
prl
+ B
1/3Bh
Spheres
n.a.
4p
r2
4/3p
r3
Ratio
of Areas and Volumes:
For similar figures with scale factor
a : b
Ratio of perimeters, sides, altitudes, any one dimensional length
a : b
Ratio of areas
a2 : b2
Ratio of volumes
a3 : b3
Triangles with congruent altitudes:
Ratio of the triangles is the ratio of the bases
Triangles with congruent bases:
Ratio of the triangles is
the ratio of the altitudes