CHAPTER 5
MEASUREMENT
SECTION 5-1
Ratios and Units of
Measure
MEASUREMENT– is a
process used to find size,
quantities, or amounts
COMPASS – is used for
drawing curved lines and
circles for measuring
distances.
PROTRACTOR – is an
instrument for measuring and
drawing angles.
SCALES or RULERS –
devices for measuring
distance.
CALIPERS and
MICROMETERS –
devices used for making
precise measurements
PRECISION – is related
to the unit of measure
used.
GREATEST POSSIBLE
ERROR – is ½ the
smallest unit used to
make the measurement.
RATIO – is a quotient of
two numbers that
compares one number
with the other.
RATE – is a ratio that
compares two different
quantities
UNIT RATE – compares
a quantity to one unit of
that quantity
SECTION 5-2
Perimeter, Circumference
and Area
PERIMETER – is the
distance around a
polygon.
CIRCUMFERENCE – is
the distance around a
circle.
AREA – the amount of
surface a figure covers.
Circle
C = d or 2r
2
A =r
Rectangle or Square
P = 2l + 2w
A = lw
Triangle
A = ½bh
Parallelogram
A = bh
Trapezoid
A = ½h(b1+b2)
SECTION 5-3
Probability and Area
PROBABILITY – the
likelihood that an event
will occur.
P(any event) =
number of favorable
outcomes ÷ number of
possible outcomes
SECTION 5-4
Problem Solving Skills:
Irregular Shapes
SECTION 5-5
Three-dimensional
Figures and Loci
POLYHEDRON– is a
three-dimensional figure
in which each surface is
a polygon and
The surfaces are called
faces. Two faces intersect
at an edge, and a vertex is a
point where three or more
edges intersect.
PRISM - a polyhedron
with two identical parallel
faces. Each of these
faces is called a base and
a prism is named by the
shape of its bases.
PYRAMID - a polyhedron
with only one base. The
other faces are triangles
that meet at a vertex and
a pyramid is named by
the shape of its base.
LATERAL FACES - are
those faces that are not
bases.
LATERAL EDGES - are
the edges of lateral faces
and can be parallel,
intersecting,or skew.
CYLINDER - a threedimensional figure having a
curved region with two
parallel congruent circular
bases. Its axis joins the
centers of the two bases.
CONE - a three-dimensional
figure having a curved
surface and one circular
base. Its axis is a segment
from the vertex to the center
of the base.
SPHERE - is the set of
points in space that are the
same distance from a given
point called the center of
the sphere.
SECTION 5-6
Surface Area of Threedimensional Figures
SURFACE AREA - The
sum of the areas of all
the faces of a threedimensional figure.
FORMULAS
Square base
A=
2
s
Square prism
SA =
2
6s
Rectangular Prism
SA = 2(lw + lh + wh)
Triangular face
A = ½bh
Circular base
A=
2
r
Curved surface
A = 2rh
Cylinder
SA = 2rh +
2
2r
Cone
SA = rs +
2
r
S is the slant height
Sphere
SA =
2
4 r
SECTION 5-7
Volume of Threedimensional Figures
FORMULAS
Prism
V = Bh
where B = area of the
given base
Pyramid
V = 1/3Bh
where B = area of the
given base
Cylinder
V=
2
r h
Cone
V=
2
1/3r h
Sphere
V=
3
4/3r
END