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 2rA =r2
Rectangle or Square
P = 2l + 2wA = 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 three-dimensional 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 Three-dimensional Figures
SURFACE AREA - The sum of the areas of all
the faces of a three-dimensional figure.
FORMULAS
Square base
A = s2
Square prism
SA = 6s2
Rectangular Prism
SA = 2(lw + lh + wh)
Triangular face
A = ½bh
Circular base
A = r2
Curved surface
A = 2rh
Cylinder
SA = 2rh + 2r2
Cone
SA = rs + r2
S is the slant height
Sphere
SA = 4r2
SECTION 5-7
Volume of Three-dimensional Figures
FORMULAS
Prism
V = Bhwhere B = area of the
given base
Pyramid
V = 1/3Bhwhere B = area of the
given base
Cylinder
V = r2h
Cone
V = 1/3r2h
Sphere
V = 4/3r3
END