Chapter 10
KV
10.1 Parallelograms and trapazoids
Parallelogram:
The base is the length of any one of the sides. The perpendicular distance between the base and oppisite side is the height
Trapezoid:
The bases of a trapezoid are its two parallel sides the perpendicular distance between the bases is the height
10.2 Circles
Diameter- distance from one side of the circle to the other crossing through the middle
Circufrence- perimeter of a circle
VOLUME (real life example)
SURFACE AREA (real life example)
10.3 three dimensional figures
Polyhedron- A solid enclosed by polygons
Face- The polygons that form the polyhedron
Prism- Two congruent bases that lie in parallel planes the other faces are rectangles
Pyramid- One base and the other faces are triangles
Cylinder- Solid with two congruent circular bases that lie in parallel planes
Cone- Solid with one circular base
Sphere- Solid formed by points in space that are the same distance from the center
Edge- Where two faces meet
Vertex- Where three or more faces meet
( names of polyhedrons are determined by the shape of the base )
Since a circle is not a polygon because it hase no straight sides a cylinder is not a polyhedron
10.4 surface area of prisms and cylinders
Surface area- The sum of the area of a polyhedrons faces
10.5 surface area of prisms and cones
Finding slat height => Use the pythagorean theorem
The heigt of a pyramid is the perpendicular distance between the vertex and base
10.6 volumes of prisms and cylinders
Volume is measured in cubic units, one cubic unit is the amount of space occupied by a cube that measures one unit on each side
the volume of a prism and a cylinder are very similar
ALL FORMULAS
circle- A=π·r^2
trapezoid- A=0.5·(b1+b2)h
square- A=bh
parallelogram- A=bh
3-D
Sphere- V=4/3π·r^3
Prism- V=Bh (l·w·h)
Cone- V=1/3 Bh
Pyramid- V=1/3 Bh
Cylinder- V=π·r^2·h
SURFACE AREA
Prism- S=2B+Ph
Cone- S=π·r^2 + πrl
Pyramid- S=B+1/2·Pl
Sphere- S= 4πr^2
Cylinder-S=2B+Ch
l= slat height
C= circumfrence
B= area of the base
S= surface area
P= perimeter of the bse
h= height
b= base
s= side length of base