CHAPTER 5 MEASUREMENT

Ratios and Units of Measure 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

Perimeter, Circumference and Area 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 A =r2

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.

number of favorable outcomes ÷ number of possible outcomes P(any event) = number of favorable outcomes ÷ number of possible outcomes

Problem Solving Skills: Irregular Shapes SECTION 5-4 Problem Solving Skills: Irregular Shapes

Three-dimensional Figures and Loci 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 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 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 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.

Surface Area of Three-dimensional Figures 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 = 2rh

Cylinder SA = 2rh + 2r2

Cone SA = rs + r2 S is the slant height

Sphere SA = 4r2

Volume of Three-dimensional Figures SECTION 5-7 Volume of Three-dimensional Figures

FORMULAS

where B = area of the given base Prism V = Bh where B = area of the given base

where B = area of the given base Pyramid V = 1/3Bh where B = area of the given base

Cylinder V = r2h

Cone V = 1/3r2h

Sphere V = 4/3r3

END