Geometry Similar Polygons, can anyone please help me?

Question

Part 1:  Plan and Make a Model 
You have been selected to design a stain glass window for the city.  It must include the following: 
1. The picture must have a design or theme.   
2. You must choose (at least) 5 different polygons.  (No curves allowed)

 

i.  Triangle            i Rhombus 

ii Quadrilateral     ii pentagon

iii Parallelogram  iii Hexagon

iv Trapezoid        iv Heptagon

v square               v Octagon

 

3. Use graph paper (8.5 by 11 in) and a straight edge to sketch your model.   
4. For each polygon

a. Label the vertices.

b. Measure the length of each side of each polygon. (You may need to use the distance formula to find the lengths.)  

 

Part 2: Actual Measurements 
After you complete your model, the city asked you to provide them with the actual measurements of your design.  Since your final piece measures 170 inches by 220 inches, you need to provide the city with the exact measurements of your design and each figure so that the city can buy all of your materials.  (Keep in mind that your original piece was on a standard sheet of 8.5 by 11 inch graph paper.)  Create a table for each polygon with your data, showing all calculations. 

 

The table should include:

1. All of the side lengths of the model.

2. The proportions and calculations that show your actual dimensions.

3. The actual dimensions of the stained glass window.

 

*An example of the table is included below.*  

Polygon #1	Model	Actual
Name:	Pentagon
Side 1:	5 in	3/23x=5/x 3x=115 x=38.33 38.33 in
Side 2:	5in	3/23x=5/x 3x=115 x=38.33 38.33 in
side 3:	7 in	3/23x=5/x 3x=115 x=38.33 38.33 in
Side 4:	10 in	3/23=10/x 3x=230 x=76.67 76.67 in
Side 5:	10 in	3/23=10/x 3x=230 x=76.67 76.67 in
Perimeter:	5 + 5 + 7 + 10 + 10 = 37 in	3/23=37/x 3x=851 x=283.67 or 38.33+38.33+53.67+76.67+76.67=283.67 in

 

Answer 1

Part (1):

1)

Consider five polygons as Square, Pentagon, Hexagon, Triangle and Parallelogram.

Draw each polygon with different themes.

Square type window:

Pentagon type window:

Hexagon type window:

Triangle type window:

Parallelogram type window:

2)

Designs a stain glass window for the city.

Consider five different polygons.

(1) Square

(2) Pentagon

(3) Hexagon

(4) Triangle

(5) Parallelogram.

Answer 2

3)

Consider the graph paper with the dimensions 11 by 8.5 in.

4)

Draw the square type window on the graph paper.

Label the vertices.

Observe the figure:

Vertices of the square ABCD are  and .

Find the length of the sides of the triangle using distance formula.

Distance between two points and is .

 in.

 in.

 in.

 in.

Draw the pentagon type window on the graph paper.

Label the vertices.

Observe the figure:

Vertices of the square ABCDE are and .

Find the length of the sides of the pentagon using distance formula.

 in.

 in.

 in. 

 in.

 in.

Draw the hexagon type window on the graph paper.

Label the vertices.

Observe the figure:

Vertices of the hexagon ABCDE are and .

Find the length of the sides of the triangle using distance formula.

 in.

 in.

in.

 in.

 in.

in.

Comments

Continued.....

Consider the graph paper with the dimensions 11 by 8.5 in.

Draw the triangle type window on the graph paper.

Label the vertices.

Observe the figure:

Vertices of the triangle ABC are and .

Find the length of the sides of the triangle using distance formula.

 in.

 in

 in.

Consider the graph paper with the dimensions 11 by 8.5 in.

Draw the Parallelogram type window on the graph paper.

Label the vertices.

Observe the figure:

Vertices of the parallelogram ABCD are and .

Find the length of the sides of the triangle using distance formula.

 in.

 in.

 in.

 in.

Answer 3

Part (2):

Step 1:

From (4): The length of the sides of the square are .

Final piece measures 170 inches by 220 inches.

Create a table for square to find the actual dimensions of the square:

 Observe the table:

The actual dimensions of the square are .

Step 2:

From (4): The length of the sides of the pentagon are and

Final piece measures 170 inches by 220 inches.

Create a table for pentagon to find the actual dimensions of the square:

Observe the table:

The actual dimensions of the pentagon are and

Step 3:

From (4): The length of the sides of the Hexagon are and

Final piece measures 170 inches by 220 inches.

Create a table for hexagon to find the actual dimensions of the square:

Observe the table:

The actual dimensions of the hexagon are and

Comments

Continued.....

Step 4:

From (4): The lengths of the sides of the triangle are  in,  in and  in.

Final piece measures 170 inches by 220 inches.

Create a table for triangle to find the actual dimensions of the triangle :

Observe the table:

The actual dimensions of the  triangle are ,  and  inches.

Step 5:

From (4): The lengths of the sides of the parallelogram are , ,  and .

Final piece measures 170 inches by 220 inches.

Create a table for parallelogram to find the actual dimensions of the parallelogram:

Observe the table:

The actual dimensions of the parallelogram are   and .

Solution:

The actual dimensions of the square are .

The actual dimensions of the pentagon are  and 

The actual dimensions of the hexagon are  and 

The actual dimensions of the  triangle are ,  and  inches.

The actual dimensions of the parallelogram are   and .