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Geometry Similar Polygons help?

0 votes

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.*  
Example of Table:  (This is done with the ratio of the model to the actual being 3 to 23.  Your ratio is different.)
Polygon#1 Model Actual
Name: Pentagon  
Side 1: 5 in
3/23=5/x
3x=115
x=38.33
38.333 in
 

 

Side 2: 5in
3/23=5/x
3x=115
x=38.33
38.333 in
Side 3: 7 in
3/23=7/x
3x=161
x=53.67
53.67 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

 

 

asked Nov 1, 2015 in GEOMETRY by anonymous

3 Answers

0 votes

Part (1):

1)

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

Draw each polygon with different themes.

Square type window:

image

Pentagon type window:

image

Hexagon type window:

image

Triangle type window:

image

Parallelogram type window:

image

2)

Designs a stain glass window for the city.

Consider five different polygons.

(1) Square

(2) Pentagon

(3) Hexagon

(4) Triangle

(5) Parallelogram.

answered Nov 2, 2015 by cameron Mentor
0 votes

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.

image

Observe the figure:

Vertices of the square ABCD are image and image.

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

Distance between two points and is .

image in.

image in.

image in.

image in.

Draw the pentagon type window on the graph paper.

Label the vertices.

image

Observe the figure:

Vertices of the square ABCDE are image and image.

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

image in.

image in.

image in

image in.

image in.

Draw the hexagon type window on the graph paper.

Label the vertices.

image

Observe the figure:

Vertices of the hexagon ABCDE are image and image.

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

image in.

image in.

image in.

image in.

image in.

image in.

answered Nov 2, 2015 by cameron Mentor

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.

image

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.

image

Observe the figure:

Vertices of the parallelogram ABCD are image and image.

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

image in.

image in.

image in.

image in.

0 votes

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 image and image

answered Nov 2, 2015 by Lucy Mentor
Continued.....

Step 4:

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

Step 5:

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

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  image and image.

Solution:

The actual dimensions of the square are .

The actual dimensions of the pentagon are  and 

The actual dimensions of the hexagon are image and image

The actual dimensions of the  triangle are imageimage and image inches.

The actual dimensions of the parallelogram are  image and image.

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