how do we calculate the area of regular polygons ?

What are regular polygons?
   
Regular polygons are polygons with all sides and all angles equal


Some examples of these are
-Pentagons
-hexagons
-heptagons 


The formula to this :


Area = (½)nas


n = number of sides
a = apothems = length of a side




  
This table shows that the formula is 1/2 times the N(number) of sides, A(apothem) and side length (R)


Example:
   Pentagons - 5 (1/2 x a s)

How do we identify solids ?

First thing we need to know is 


What is a solid ?


A solid is a 3D or three dimensional shape that has a height, width and depth

* There are 2 main types of solids 

     

     - Polyhedra

     - Non - Polyhedra 

Polyhedra 's must have flat faces 

    Examples: Prisms, and Pyramids

Non- Polyhedra's are if any surface isnt flat 

    Examples:

What is isometry ?

An isometry is a transformation where the original figure and its image are congruent.

Types of isometry                    Not a type

        -  Reflection                             -  Dilation 
        -  Rotation   
       -  Translation  

• The reason why dilation isn't a isometry is because the original image is either shrunk or enlarged.

Examples:

    

Reflection

Rotation 

Translation



Practice Question :


What is the type of isometry in the given figure ?

A) Rotation

B) Reflection

C) translation

D) Dilation

Answer : C Translation

How do we solve more complex area problems?

As for example:

 

  Example: 

                    

First you look at your trapezoid & write down the measurements for its bases & its height in order to find your area

Formula: A = 1/2 h (b1+b2)

lets say these were the measurements..

Base1: 3ft

Base2: 8ft

Height:5ft

Area: 1/2h(b1+b2)

Area: 1/2 x 5 (3+8)

Area: 1/2 x 5 (11)

Area: 1/2 x 55

Area: 27.5 ft squared

How do we find the area of a regular polygon?

First we look at our polygon

Example: 
                
Next you look at your formula & start finding the area of the polygon

Formula: A= nas/2


*Make sure you use your formula correctly 

how do we find the area of parallelograms,kites,and rapezoids

Area of a parallelogram 

•  Base x Height 

Area of a trapezoid

• A = 1/2 h (b1+b2)

Area of kites 

• A = d1 d2 / 2

How do we use the other definitions of transformations?

Glide Reflection: Combinations of a reflection in a line and a translation along that line.

Orientation: Refers to the arrangement of points, relative to one another after transformation.


Isometry: A image that the length an size stays the same

Direct Isometry: the orientation letters & length stay the same


Oppisite Isometry: Letters are backwards but same length a reflection.