Rules for Finding Area
Square Region
Area = side x side
A = s2
Rectangular Region
Area = length x width (or base x height)
A = lw (or bh)
s
w (h)
l (b)
s
Parallelogram and Rhombus Regions
Area = base x height
A = bh
Trapezoidal Region
Area = 1/2 x sum of parallel sides lengths
x height
A = 1/2 (a + b)h
a
h
h
b
b
Triangular Region
Area =
A =
1
2
1
2
Circular Region
Area = Pi x radius x radius
A = r2
x base x height
bh
r
h
b
Elliptical (Oval) Region
Area = Pi x a x b
A = ab
a
b
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Rules for Finding Surface Area
Sphere
A = 4�r 2
Cube
Area = 6 x Area of one face
A = 6s 2
r
s
s
Cylinder
Area= (2 x area of base) + Area of curved surface
= (2 x area of base) + (circumference of circular region x height)
A= 2�r 2 + 2�rh
r
h
Rectangular Prism
Area = 2lw + 2lh + 2wh
h
l
w
Cone
Area = Area of base + Area of curved surface
A= �r 2 + �rs
h
s
r
Hemisphere
1
Area= 2 x (Area of sphere) + Area of circular region
1
= 2 (4�r 2) + �r 2
= 2�r 2 + �r 2
= 3�r 2
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Rules for Finding Volume of Prisms
General Rule for All Prisms and Cylinders
Volume = Area of base x height of prism or cylinder
Rectangular Prism
Volume = length x width x height
Cube
Volume = length x width x height
=sxsxs
V = s3
=lxwxh
V = lwh
s
h
w
l
s
Triangular Prism
Volume = Area of base x height of prism
1
= 2 x base of triangle x height of
triangle x height of prism
1
= ( 2 x b x h) x l
V =
1
2
Trapezoidal Prism
Volume = Area of base x height of prism
1
= 2 x sum of parallel side lengths
of prism trapezoid x height of
trapezoid x height of prism
1
= [ 2 (a + b) x h] x l
bhl
V=
Note: For triangular prisms, two heights are
involved, the height (h) of the triangular base
and the height (l) of the prism.
1
2
(a + b)hl
Note: For trapezoidal prisms, two heights are
involved, the height (h) of the trapezoidal
base and the height (l) of the prism.
h
h
b
s
l
a
b
l
Cylinder
Volume = Area of base x height
= r2 x h
V = r 2h
r
h
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Rules for Finding Volume of Pyramids & Spheres
General Rule for All Pyramids and Cones
Volume =
1
3
x area of base x height of a pyramid or cone
Rectangular Pyramid
1
Volume= 3 x area of base x height
=
V=
1
3
1
3
Volume=
xlxwxh
lwh
=
V=
1
3
1
3
1
3
Square Pyramid
x area of base x height
xlxlxh
l 2h
h
h
w
l
Triangular Pyramid
Volume=
V=
1
3
1
3
x area of base x height
x
1
2
l
l
Volume=
=
lxwxh
h
V=
1
3
1
3
1
3
Cone
x area of base x height
x �r 2 x h
�r 2h
h
l
w
r
Sphere
Volume=
4
3
�r 3
r
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