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