Chapter 10

Jamie W.

Section 10.1

Area of a Parallelogram

  • Formula: A=b x h
  • Base multiplied by height





Area of a Trapezoid

  • Formula: A=1/2(b1+b2)h
  • Base 1 and Base 2 are the two bases, doesn't matter which is which
  • Add base 1 and base 2 together, then multiply by the height, then multiply by 1/2
  • Height on a slant, perpendicular to the base




Area of Squares

  • Formula: A=b x h
  • Base times height
  • Same as parallelogram





Area of a Triangle

  • Formula: 1/2 x b x h
  • Half times base times height
  • Square/Parallelogram divided by 2

Section 10.2

Area of a Circle


  • Formula: pi x radius squared
  • pi= 3.14, 22/7, or pi button




The following video explains how to get the area of a circle clearly. It also shows that if you only have the diameter of the circle, you can still figure out the area by dividing the length of the diameter by 2 to get the radius.

Area of a Circle - MathHelp.com - Math Help

Section 10.3

Solids Classification



Prisms:


  • have two congruent bases (same size, same shape)
  • other faces are rectangles
  • named by the shape of it's base (i.e: rectangular prism)




Pyramids:
  • has one base, that is a certain shape like a prism
  • named for shape of it's base (i.e: triangular pyramid)
  • other faces are triangles
  • faces come to a vertex at the top




Cylinder:

    • has two congruent bases
    • bases always circular
    • bases always parallel
    • no faces, edges, or vertices


More Solids


Cone:


  • has one circular base
  • no faces or edges
  • lateral surface comes to point at top
  • similar to pyramid, only circular and no triangular faces






Sphere:


  • basically a ball
  • formed by all points in space that are the same distance from a fixed point called the center

Cone

This is a cone, where there is one circular base and one lateral surface.
Big image
D1 2D Representations of Solids

Section 10.4

Surface Area of a Prism

Formula:

s=2B+Ph


Area of the base multiplied by 2,

plus the perimeter times the height

Surface Area of a Cylinder

Formula:

s=2B+Ch=2*pi*r^2+2*pi*r*h


Area of the base multipied by 2,

plus the circumference times the height


Circumference: 2*pi*radius



The following video clearly teaches you about the surface area of prisms and cylinders.

Solving for Surface Area of Retangular prisms, Right Triangular prisms and Cylinders

Section 10.5

Surface Area of a Pyramid

Formula:

B+1/2Pl


Area of the base,

plus one half the product

of the perimeter and the slant height.

surface area of a cone

Formula:

pi*r^2+pi*r*l


Area of the base (pi*r^2)

plus the product of pi times

the radius times the slant height

Section 10.6

Volume is the amount of space that an object occupies.

Volume of a prism

Formula:

Bh


area of the base

times the height.

Volume of a Prism - MathHelp.com - Math Help

volume of a cylinder

Formula:

Bh


area of the base (pi*r^2)

times the height

Section 10.7

volume of a pyramid

Formula:

1/3Bh


area of the base multiplied

by the height, times one third.

Volume of a cone

Formula:

1/3*Bh=1/3*pi*r^2*h


area of the base times the height,

multiplied by one third.


area of the base: pi*radius^2

Real Life Tie-Ins

Big image
These are some examples of geometry in real life.

Some of the most modern examples are:


  • The Equator and Prime Meridian (perpendicular lines)
  • Hershey's Kiss (cone)
  • Pyramids of Egypt (pyramid)

Wrap Up

I hope this Smore makes you sucessful on the test!