math 104 - test #4

customary system

inches (in), feet (ft), yards (yd), miles (mi)

metric system

uses powers of 10; millimeters (mm), centimeters (cm), decimeters (dm), meters (m), dekameter (dam), hectameter (hm), kilometers (km)

perimeter

sum of all side lengths of a polygon

rectangle and square perimeter

P = 2w + 2l

circle perimeter (circumference)

C = 2(pi)(r)

area of rectangle and parallelogram

A = bh (base x height)

area of square

A = s²

area of triangle

A = ½ bh (1/2 base x height)

area of trapezoid

½ x height x (sum of bases)

area of a circle

A = (pi)r²

how to classify solids (polyhedron)

1. by bases (single base is a polygon, 2 bases are congruent/parallel polygons)

2. by faces (sides of the solid; 1 base = triangle faces, 2 bases = rectangle (right solid) or parallelogram (oblique solid))

3. by vertex (points of a solid; point where bases and faces intersect)

4. by edges (the intersection of base and face and intersection of faces)

right solid

faces are perpendicular to the bases or the vertex is perpendicularly above the center of the base (think cube)

oblique solid

faces are NOT perpendicular to the bases or vertex is NOT perpendicularly above the center of the base

base area of rectangular prism

B = lw (length x width)

lateral area of rectangular prism

sum of face areas, (lw)+(lw)+(lw)+(lw)

{ex: 15 length, 3 height, 5 width (15×3)+(15×3)+(15×3)+(15×3) = 120}

total area of rectangular prism

2B + LA

base area of a cylinder

B = (pi)r²

2B = 2(pi)r²

lateral area of a cylinder

area of “sides”

2(pi)rh

base area of square pyramid

B = s²

slant height

lateral area of pyramid

½ pl (1/2 x perimeter x slant height)

total area of a pyramid

TA = B + LA

base area of a cone

B = (pi)r²

lateral area of a cone

LA = (pi)rh

total area of a cone

TA = B + LA

area of a sphere

A = 4(pi)r²

area of a hemisphere

A curve = 2(pi)r²

A entire solid = 3(pi)r²

volume

the space “inside”, the capacity of the solid, how much the solid holds

• units are cubed ( ex: cm ³)

volume of prisms and cylinders

V = Bh

volume of pyramids and cones

V = 1/3 Bh

volume of sphere

V = 4/3 (pi)r³

units of capacity

ounce (oz), cup (c), pint (pt), quart (qt), gallon (g, gal)

units of mass

ounce (oz), pound (lb or #), ton (t)