How do we identify solids?

           Solid Geometry, Lateral Area & Surface Area 
Solid Geometry ; 

  Solid geometry is the geometry of 3 - dimensional spaces.  It is called three dimensional , or 3D because there are three dimensions width , length and height. 

Solids have properties that are special  :
 - Surface Area ( think of the area of the faces and curved surface of a solid figure)

              - Volume ( Think about how much water the figure can hold )

There are two types of solids :

            - Polyhedra

            - Non- Polyhedra 

     

Polyhedra includes Prisms, Pyramids and Platoric Solids 

There are many different types of Prisms

Non- Polyhedra includes Spheres, Cylinder, Cones and Torus 

Torus

Sphere 

Cylinder 

Cone

Lateral Area & Surface Area 

Lateral Area is the sum of the areas of the lateral (vertical) faces of a cylinder, cone and more

Surface 

A Prism has the same cross section all along it`s length!

Surface Area = area of the bases + Lateral Area ( area of the sides )

A cross section is the shape you get when cutting straight across an object 

A Pyramid is a solid that contains a polygon base to point 

the slant height of a pyramid is the height of one of the lateral faces 

L.A = 1/2pt * 4

Surface Area = L.A + B( area of the bottom) 

Cones : the base of a cone is a circle and the other end (vertex) is the "pointed" similar to a pyramid 

The slant height of a cone is the distance from the vertex to a point on the edge of a base 

L.A = πrl   ( r means radius, and l means Slant height)

B = πr^2 

Surface Area = L.A + B

A Cylinder is a geometric figure with straight parallel sides and a circular or oval base 

L.A = 2πh or πdh

Surface Area = Lateral Area + Area of a Circle 

Surface Area = 2πh + 2πr^2

How do we graph transformations that are dilation?

What Is Dilation?

Dilation: An enlargement or shrinking of a figure by a given scale factor produces similar figures 

What does the symbol of dilation look like? 
    Notation: Dn where n represents the scale factor rule for a dilation with a scale factor of n

        For Example: (X,Y)  -> ( nX, nY)
                              A`( 2, 4)->(4,8) when the scale factor is 2
   First Step is to multiple the X value by the scale factor
    Second Step is t multiple the Y value by the scale factor
   Then you get the "copy" of the original figure

       Watch this video below for more help on this topic

                                                                                                                                                                                   If the scale factor, N, is greater than 1, the image is an enlargement (a stretch).
If the scale factor is between 0 and 1, the image is a reduction (a shrink).

 Most dilation's in coordinate geometry use the origin, (0,0), as the center of the dilation.

For Example :

PROBLEM:  Draw the dilation image of triangle ABC with the center of  dilation at the origin and a scale factor of 2.

OBSERVE: Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2).

HINT: Dilation involve multiplication!

Example 2: 

PROBLEM:  Draw the dilation image of pentagon ABCDE with the center of  dilation at the origin and a scale factor of 1/3.

OBSERVE: Notice how EVERY coordinate of the original pentagon has been multiplied by the scale factor (1/3).

HINT: Multiplying by 1/3 is the same as dividing by 3!